Representing Square Numbers Copyright © 2009 Nelson Education Ltd

Representing Square 1.1 Numbers Student book page 4

You will need Use materials to represent square numbers. • counters A. Calculate the number of counters in this square array. • a calculator number of number of number of counters counters in counters in in a row a column the array 25 is called a square number because you can arrange 25 counters into a 5-by-5 square. B. Use counters and the grid below to make square arrays. Complete the table.

Number of counters in: Each row or column Square array 525

Is the number of counters in each square array a square number?

How do you know?

NNEL-MATANSWER-08-0702-001-L01.inddEL-MATANSWER-08-0702-001-L01.indd 8 99/15/08/15/08 5:06:275:06:27 PMPM C. What is the area of the shaded square on the grid? Area s s s units units square units s When you multiply a whole number by itself, the result is a square number. Is 6 a whole number? So, is 36 a square number? D. Determine whether 49 is a square number. Sketch a square with a side length of 7 units. Area units units square units Is 49 the product of a whole number multiplied by itself? So, is 49 a square number?

The “square” of a number is that number times itself. For example, the square of 8 is 8 8 . 8 8 can be written as 82 (read as “eight squared”). terms 64 is a square number. whole numbers the counting numbers that begin at 0 and E. Square 9 and 10. continue forever 2 (0, 1, 2, 3, …) 9 9 or 9 10 10 or 102 square number the product of a Are both of these products square numbers? whole number How do you know? multiplied by itself

F. Identify two square numbers greater than 100. 2 ( ) 2 ( )

NNEL-MATANSWER-08-0702-001-L01.inddEL-MATANSWER-08-0702-001-L01.indd 9 99/15/08/15/08 5:06:285:06:28 PMPM Recognizing Perfect 1.2 Squares Student book pages 5–9

You will need Use materialsa variety of to strategies represent tosquare identify numbers. perfect • a calculator squares.

Method 1: Using diagrams The area of a square with a whole-number side length is a 9 units perfect square. This 9-by-9 square has an area terms 9 units of square units, so is perfect square (or a perfect square. square number) the square of a whole Method 2: Using factors number PROBLEM A perfect square can be written as the product prime factor of 2 equal factors. Is 225 a perfect square? a factor that is a prime Draw a tree diagram to identify the prime factors of 225. number Continue factoring until the end of each branch is a prime A prime number has number. only itself and 1 as factors. 225 The ones digit of 225 is , so The ﬁ rst few prime 5 is a factor of 225. numbers are 2, 3, 5, 7, The factor partner is 225 ÷ 5 . 11, 13, 17, …. 5 225 5

45 is not a prime number, because 9 45. 9 45 9 9 is not a prime number, because 9 3 . 9 3

The ends of the branches are now all prime numbers: 5, 5, 3, and 3. Write 225 as the product of these prime factors.

NNEL-MATANSWER-08-0702-001-L02.inddEL-MATANSWER-08-0702-001-L02.indd 1100 99/16/08/16/08 11:28:21:28:21 AMAM 225 5 Group the prime factors to create a pair of equal factors. 225 5 5 3 3 (5 3) ( ) 2 15 or ( ) Is 225 the square of a whole number? So, is 225 a perfect square?

170 PROBLEM Is 170 a perfect square? Complete the tree diagram.

Write 170 as a product of prime factors. 17 170 17 Can you group the prime factors to create a pair of equal factors? So, is 170 a perfect square? 2 Method 3: Look at the ones digit

Whole Perfect The table shows the fi rst 10 perfect squares. number square Circle the possible ones digits for a perfect square. 00 1 1 0 1 2 3 4 5 6 7 8 9 2 4 Look at the ones digit of 187. Could 187 be a perfect 3 9 square? 4 16 5 25 A number with ones digit 0, 1, 4, 5, 6, or 9 may or may not 6 36 be a perfect square. 7 49 Look at the table of the fi rst 10 perfect squares. Is 6 a 8 64 perfect square? Is 36 a perfect square? 9 81 10 100 Refl ecting Show that 400 is a perfect square without using a drawing or tree diagram. 2 4 (2)2, so 400 ( )

NNEL-MATANSWER-08-0702-001-L02.inddEL-MATANSWER-08-0702-001-L02.indd 1111 99/16/08/16/08 11:28:21:28:21 AMAM Practising 3. The area of this square is 289 square units. Is the side length a whole number? 17 units So, is 289 the square of a whole number? So, is 289 a perfect square? 4. Show that each number is a perfect square. 17 units a) 16 Sketch a square with an area of 16 square units. Side length of the square units Is the side length a whole number? So, is 16 a perfect square? b) 1764 Represent the factors of 1764 in a tree diagram. Use divisibility rules to help you identify factors.

1764 Divisibility rules

• If the number is 2 even, 2 is a factor. • If the sum of the digits is divisible by 2 3, then 3 is a factor. • If the sum of the digits is divisible by 9 9, then 9 is a factor.

Write 1764 as a product of prime factors. 1764 Group the factors to create a pair of equal factors. 1764 ( ) ( ) 2 or ( ) Is 1764 a perfect square?

NNEL-MATANSWER-08-0702-001-L02.inddEL-MATANSWER-08-0702-001-L02.indd 1122 99/16/08/16/08 11:28:21:28:21 AMAM 2025 7. Maddy started to draw a tree diagram to determine whether 2025 is a perfect square. 5 405 How can Maddy use what she has done so far to determine that 2025 is a perfect square? 581 Solution:

99 Write 2025 as the product of the factors at the ends of the branches in Maddy’s tree diagram. 2025 These factors are not all prime numbers, but you can rearrange them to create a pair of equal factors. 2025 ( ) ( ) 2 or ( ) Is 2025 the square of a whole number? So, is 2025 a perfect square? 8. Guy says: “169 is a perfect square when you read the digits forward or backward.” Is Guy correct? Explain. Solution: Use the strategy of guess and test. 102 , so 169 is than 102. Try some squares greater than 102. 112 122 132 Is 169 a perfect square?

Hint 169 written backward is . Use 32 9 to solve 302 , so 961 is than 302. 2 ■ 30 . Try 312. 312 Is 961 a perfect square? Explain why 169 and 961 are perfect squares.

NNEL-MATANSWER-08-0702-001-L02.inddEL-MATANSWER-08-0702-001-L02.indd 1133 99/16/08/16/08 11:28:22:28:22 AMAM Square Roots of 1.3 Perfect Squares Student book pages 10–15

You will need Use a variety of strategies to identify perfect • a calculator squares.

A square has an area of 16 m2. Determine the side length, s. Area of a square s2 Area = 16 m2 Solve s2 16 m.

Which whole number multiplied by s metres itself equals 16? So, s m. 4 is called the square root of 16, because 42 16. term ___ − Ί square root (√ ) Using the square root symbol, 4 16. one of 2 equal factors − of a number Determine √ 144 by guess and test. 2 For example, the PROBLEM A square has an area of 144 m . Determine the square root of 25 is 5, ____ side length, s Ί144 . because 52 25. Solve the related equation s2 144. Using___ the symbol, Ί 25 5. Use the strategy of guess and test. A = 144 m2 Notice that ______102 202 Ί 25 Ί 25 25. 144 is between 100 and 400. s metres So, s2 is between 102 and ( )2. Is 144 closer to 100 or 400? So, is s2 closer to 102 or 202? Square 11. 112 Square 12. 122 ____ s2 144, so s Ί144 m.

NNEL-MATANSWER-08-0702-001-L03.inddEL-MATANSWER-08-0702-001-L03.indd 1144 99/16/08/16/08 11:30:08:30:08 AMAM − Determine √ 225 by factoring. This factor rainbow shows all the factors of 225. Complete the table to show the factor partners. 1 3 5 9 15 15 25 45 75 225 The factor with an equal partner is √225 the square root. Factors of 225 15 15 225 0 225 ____ So, Ί 225 . 3 A perfect square is the square of a 5 whole number. Is 225 the square of a whole 9 number? 15 Is 225 a perfect square?

− Determine √ 256 using factors. 256 Complete the tree diagram of the factors of 256. Then, write 256 as a product of prime numbers. 2 256 Group these factors to create a pair of equal factors. 4 256 ( ) ( ) ( )2 2 ____ So, Ί 256 .

2 Reﬂ ecting How can you check your answer when you calculate the square root of a number? ___ 4 Use Ί 81 9 and 92 81 to explain.

NNEL-MATANSWER-08-0702-001-L03.inddEL-MATANSWER-08-0702-001-L03.indd 1155 99/16/08/16/08 11:30:08:30:08 AMAM Checking 2. Calculate. __ a) Ί 4 If the area of a square is 4 square units, then the A = 4 m2 side length of the square is units. __ Ί 4 ___ b) Ί 16 A = 16 m2 If the area of a square is 16 square units, then the side length of the square is units. ___ Ί 16 ___ c) Ί 81 If the area of a square is 81 square units, then the side length of the square is units. ___ Ί 81

A = 81 m2 Practising 3. a) Complete the factor rainbow. 441 ÷ 7 , so 7 441. The factor partner for 7 is . 441 ÷ 9 , so 9 441. 1 3 7 9 21 147 441 The factor partner for 9 is . 441 ÷ 21 , so 21 441. The factor partner for 21 is .

b) Is 9 the square root of 441? Why or why not?

Which factor of 441 is the square root? ____ Ί441 c) Square the square root to check your answer.

( )2

NNEL-MATANSWER-08-0702-001-L03.inddEL-MATANSWER-08-0702-001-L03.indd 1166 99/16/08/16/08 11:30:09:30:09 AMAM ____ 15. Describe 2 strategies to calculate Ί324 . Guess and test 102 202 Is 324 closer to 100 or 400? ____ 2 2 So, Ί324 is closer to ( ) than to ( ) . Guess the number whose square is 324. Square the number. ( )2

If the number you guessed is not the square____ root, continue guessing until you identify Ί 324 . ( )2 ( )2 ____ So, Ί324 .

Factoring 324 Represent the factors of 324 in a tree diagram. Use divisibility rules to identify Divisibility rules factors of 324. • If the number is Write 324 as a product of prime even, 2 is a factor.

numbers. • If the sum of the digits is divisible by

324 3, then 3 is a factor.

• If the sum of the Group the factors to create a digits is divisible by pair of equal factors. 9, then 9 is a factor.

324 ( ) ( ) or ( )2 ____ So, Ί324 .

NNEL-MATANSWER-08-0702-001-L03.inddEL-MATANSWER-08-0702-001-L03.indd 1177 99/16/08/16/08 11:30:09:30:09 AMAM 1.4 Estimating Square Roots Student book pages 16–20

You will need Estimate the square root of numbers that are • a calculator not perfect squares.

If a number is not a perfect square, you can estimate its square root. − Estimate √ 10 by comparing it to roots of perfect squares. Estimate the side length of a square with an area of 10 square units. Step 1: On the grid paper, draw a 2-by-2 square, a 3-by-3 square, and a 4-by-4 square. 2 Complete the table. ( )

Square Side length Area Side length__ (s) (s2) ( A) __ 2-by-2 24 4

____ 3-by-3 _____ 4-by-4

Step 2: Use the side___ lengths of the squares you drew to estimate 10. __ 4 2 ___ __ 9 10 is between and , ___ and closer to than . 10 ■ ______So, 10 is not a whole number. 16 ___ Step 3: Determine 10 to 2 decimal places. Square 3.1. 3.12 (too low) Square 3.2. 3.22 (too high) The square of 3.2 is close to 10. ___ So, 10 is approximately .

NNEL-MATANSWER-08-0702-001-L04.inddEL-MATANSWER-08-0702-001-L04.indd 1188 99/16/08/16/08 11:31:10:31:10 AMAM Determine square roots using a calculator. __ Calculators have a square root button, . Different calculators use different key sequences. ___ PROBLEM Calculate 10 . Round the result to 3 decimal places. Try each sequence below. __ __ 10 or 10

Circle the sequence above that works with your calculator. ___ Communication Tip 10 ᝽ ____ The symbol “᝽ ” PROBLEM Calculate 0.5 300 . means “approximately ______equal to.” 0.5 300 means the same as 0.5 300 . ____ When you round a First, estimate 0.5 300 . Use mental math. number, the answer ______is an approximation. Step 1: Use 100 10 and 400 20 to estimate 300 . ____ Use “᝽ ” instead of “” 300 ᝽ when you write your ______ answer. Step 2: 0.5 300 is half of 300 . Halve your estimate in step 1. ____ 0.5 300 ᝽ ____ Now, calculate 0.5 300 . Use a calculator. __ __ 0.5 300 or 0.5 300

Round the result to 4 decimal places. ____ 0.5 300 ᝽

Reﬂ ecting 8.6603 and 8.6602 are both the same distance from 8.66025. Why is it more likely that you chose 8.6603 when rounding 8.66025 to 4 decimal places?

Hint ___ 2 The symbol means 10 ᝽ 3.162, but 3.162 10. Why is this? “is not equal to.”

NNEL-MATANSWER-08-0702-001-L04.inddEL-MATANSWER-08-0702-001-L04.indd 1199 99/16/08/16/08 11:31:10:31:10 AMAM Practising 4. Estimate to determine whether each answer is reasonable. Correct any unreasonable answers using the square root key on your calculator. ___ a) 10 ᝽ 3.2 The area of a square with side length 3 units is square units. The area of a square with side length 4 units is square units. Hint Is 3.2 a reasonable estimate for the square root of 10? Use the correct key sequence for your Use your calculator to check. calculator. ___ 10 ᝽ For example,___ to ___ calculate 10 , use b) 15 ᝽ 4.8 either 10 or The area of a square with side length 4 units is 10 . square units. The area of a square with side length 5 units is square units. Is 4.8 a reasonable estimate for the square root of 15? Use your calculator to check. ___ 15 ᝽ 5. Calculate each square root to 1 decimal place. Choose one of your answers and explain why it is reasonable. ______a) 18 ᝽ c) 38 ᝽ ______ ᝽ ᝽ b) 75____ d) 150 ᝽ is reasonable because

NNEL-MATANSWER-08-0702-001-L04.inddEL-MATANSWER-08-0702-001-L04.indd 2200 99/16/08/16/08 11:31:10:31:10 AMAM 8. Tiananmen Square in Beijing, China, is the largest open “square” in any city in the world. It is actually a rectangle of 880 m by 500 m. a) What is the approximate side length of a square with the same area as Tiananmen Square? Solution: What is the area of Tiananmen Square? Area length width m m m2

What______is the side length of a square with this area? ᝽ m b) 6002 7002 Explain how you know your answer to part a) is reasonable.______ ᝽ m is reasonable because . 10. Estimate the time an object takes to fall from each height using this formula: ______time (s) ᝽ 0.45 height (m) Record each answer to 1 decimal place.

a) 100 m _____ time ᝽ 0.45 ᝽ s

b) 200 m _____ time ᝽ ᝽ s

c) 400 m _____ time ᝽ ᝽ s

NNEL-MATANSWER-08-0702-001-L04.inddEL-MATANSWER-08-0702-001-L04.indd 2211 99/16/08/16/08 11:31:10:31:10 AMAM Exploring Problems Involving 1.5 Squares and Square Roots Student book page 24

You will need Create and solve problems involving a • square tiles perfect square. How many tiles are in each diagram?

3 ϫ 3 ϭ 9 • a calculator (3)2 ϭ 9 tiles

ϫ ϩ ϭ

2 ( ) ϩ ϭ tiles

ϫ ϩ ϭ

2 ( ) ϩ ϭ tiles

PROBLEM Joseph had 12 tiles. He made a square with ? some tiles and had 3 tiles left over. What is the side length of the square? Solve s 2 ϩ 3 ϭ 12. What number added to 3 makes 12? What is the square root of that number? 2 So, ( ) ϩ 3 ϭ 12. s ϭ tiles

PROBLEM There are 104 tiles. What is the side length ? of the square? Let the variable s represent the unknown side length. s2 ϩ 4 ϭ 104 Write an equation. s 2 ϩ 4 Ϫ ϭ 104 Ϫ Subtract 4 from each s 2 ϭ side of the equation to isolate the variable. ____ So, s ϭ Ί100 ϭ . Side length ϭ tiles

NNEL-MATANSWER-08-0702-001-L05.inddEL-MATANSWER-08-0702-001-L05.indd 2222 99/15/08/15/08 5:27:165:27:16 PMPM PROBLEM A game is played with a deck of 52 square cards. You deal the cards in equal rows and equal columns to form a square. Three cards are left over and not used. What is the side length of the square of cards? Solution: Draw a diagram similar to the ones on the previous page to represent the problem.

Choose a variable to represent the side length. Write an equation to represent the situation.

( )2 ϩ ϭ Solve the equation.

The side length of the square of cards is cards.

PROBLEM Create a problem that uses a square number and another whole number. Hint Use one of these problem-solving strategies: • Make a model • Work backward Solve the problem.

NNEL-MATANSWER-08-0702-001-L05.inddEL-MATANSWER-08-0702-001-L05.indd 2323 99/15/08/15/08 5:27:175:27:17 PMPM 1.6 The Pythagorean Theorem Student book pages 26–31

You will need Model, explain, and apply the Pythagorean • counters theorem.

On each right triangle • label the hypotenuse c • cutout 1.6 • label the smallest leg a • label the other leg b terms right triangle Pythagorean Theorem a triangle with 1 right angle (90) In a right triangle, the square of the length of the hypotenuse hypotenuse The hypotenuse is a the longest side of a is equal to the sum of the squares c leg right triangle, the of the lengths of the 2 legs. side opposite the b leg right angle. c2 a2 b2 or a2 b2 c2 The 2 shorter sides are called the legs. Use the Pythagorean theorem to determine if the triangle below is a right triangle. length of hypotenuse: c length of shortest leg: a 12 m 15 m length of other leg: b Check if a2 b2 c2. 9 m Hint To calculate 92 using Is a2 b2 c2 true for this triangle? a calculator: So, is the triangle a right triangle? 9 x2

NNEL-MATANSWER-08-0702-001-L06.inddEL-MATANSWER-08-0702-001-L06.indd 2424 99/15/08/15/08 5:29:135:29:13 PMPM Is the Pythagorean theorem true for all types of triangles? Use Cutout 1.6, which shows 2 acute triangles, 1 right triangle, and 2 obtuse triangles. Each triangle has one side 60 mm long and another side 80 mm long. A. Measure the third side of each triangle to the nearest millimetre. Record the length on the cutout page. B. Write the missing side lengths (a, b, or c) in the table. Calculate the missing squares (a2, b2, or c2).

Triangle a b a2 b2 a2 ؉ b2 c c2 Comparison A 60 80 3600 6400 10 000 a2 b2 c2 B 60 3600 80 6400 a2 b2 c2 C 60 80 3600 6400 10 000 a2 b2 c2 D 60 80 3600 6400 10 000 a2 b2 c2 E 60 3600 80 6400 a2 b2 c2

Hint C. For each triangle, calculate a2 b2 and c2. greater than Compare the 2 values. less than Record each comparison in the table. Use <, , or >. D. Is the Pythagorean theorem true for all types of Hint triangles? Explain. In the table above, A and B are acute, C is a right triangle, and D and E are obtuse. Reﬂ ecting Match the type of triangle with the equation or inequality. Acute triangle a2 b2 < c2 Right triangle a2 b2 > c2 Obtuse triangle a2 b2 c2

NNEL-MATANSWER-08-0702-001-L06.inddEL-MATANSWER-08-0702-001-L06.indd 2525 99/15/08/15/08 5:29:135:29:13 PMPM Practising 3. Herman formed a triangle with grid-paper squares. How can you tell that he formed a right triangle? Solution: The side lengths of the 3 squares and the 3 side lengths of the triangle are the same. If c2 a2 b2, then the triangle is a right triangle. c is the length of the longest side: units a and b are the other 2 side lengths: and units c2 a2 b2

( )2 ( )2 ( )2 Is the triangle a right triangle? 5. A Pythagorean triple is any set of 3 whole numbers, a, b, and c, for which a2 b2 c2. Show that each set of numbers is a Pythagorean triple. a) a 5, b 12, and c 13 a2 b2 c2 ()2 ( )2 ( )2 b) a 7, b 24, and c 25 ()2 ( )2 ( )2 c) a 9, b 40, and c 41 ()2 ( )2 ( )2

NNEL-MATANSWER-08-0702-001-L06.inddEL-MATANSWER-08-0702-001-L06.indd 2626 99/15/08/15/08 5:29:135:29:13 PMPM 7. About how far would a hockey puck travel when shot from one corner of the rink (at the goal line) to the opposite corner (at the goal line)? Think of the rink as a rectangle divided into 2 right triangles. 26 m path of puck

54 m Label the sides of the shaded right triangle a, b, and c in the diagram above. a m b m Use the Pythagorean theorem to calculate the distance, c, travelled by the puck. Round your answer to the nearest whole number. Step 1: Step 2: __ c2 a2 b2 c Ί c2 ______Hint 2 2 ( ) ( ) Ί Check a square root by multiplying it by ᝽ m __ __ Ί Ί itself. n n should be close to n. The puck would travel approximately m. 9. Calculate the unknown side to 1 decimal place. 2 2 2 9.0 cm a b c a c cm b cm 8.0 cm Hint Step 1: Step 2: ___ The original a2 b2 c2 a Ίa2 measurements are ___ precise to a tenth 2 2 2 Ί of a centimetre, so a ( ) ( ) round your answer a2 ᝽ cm the nearest tenth of a 2 centimetre. a

NNEL-MATANSWER-08-0702-001-L06.inddEL-MATANSWER-08-0702-001-L06.indd 2727 99/15/08/15/08 5:29:145:29:14 PMPM Solve Problems Using 1.7 Diagrams Student book pages 32–35

You will need Use diagrams to solve problems about • a calculator squares and square roots.

Joseph is building a model of the front of a Haida longhouse. • a ruler He wants the model to have the measurements shown on the illustration. How can Joseph calculate length c (at the top of the model)?

Solve a problem by identifying a right triangle 1. Understand the Problem Draw a diagram that includes all you know about the model. c represents the length you want to know. Complete the diagram.

c c

cm cm

NNEL-MATANSWER-08-0702-001-L07.inddEL-MATANSWER-08-0702-001-L07.indd 2288 99/16/08/16/08 11:34:15:34:15 AMAM 2. Make a Plan Draw a line on your diagram to connect the 2 dots at the tops of the sides of the model. This will make 2 right triangles at the top of the model.

The base of each triangle is half of 60 cm, or cm. The height of the triangles is the height of the whole model minus the height of the side: 30 cm cm cm Write these lengths on your diagram.

Now you know 2 sides of each triangle. Which theorem can you use to calculate the length of the unknown side of the triangle, c?

3. Carry Out the Plan Hint Write the equation that relates the sides of a right triangle. c2 The hypotenuse (the longest side) Side c in the right triangle is unknown. in a right triangle is always labelled c. The lengths of the other 2 sides are known. Use one of these lengths for a and one for b. a cm b cm Calculate c. Step 1: Step 2: __ c2 a2 b2 c Ί c2 _____ 2 2 ( ) ( ) Ί ᝽ m c is approximately cm long.

Reﬂ ecting How did drawing a diagram help solve the problem?

NNEL-MATANSWER-08-0702-001-L07.inddEL-MATANSWER-08-0702-001-L07.indd 2299 99/16/08/16/08 11:34:16:34:16 AMAM Practising

term 5. The diagonal of a rectangle is 25 cm. diagonal The shortest side is 15 cm. In a 2-D shape, a What is the length of the other side? diagonal can join any Solution: 2 vertices that are not next to each other. Draw a rectangle. Write cm beside the shortest side.

diagonal

diagonals

Draw a diagonal on the rectangle. Write cm beside the diagonal.

What does the problem ask you to determine?

Is the unknown length a side of a right triangle? Shade one of the right triangles formed by the diagonal. The hypotenuse, c, cm. Call the shortest side of the triangle a, so a cm. The unknown side is b. Use the Pythagorean theorem to calculate the other side length. Step 1: Step 2: ___ a2 b2 c2 b Ίb2 _____ 2 2 Ί () b2 ( ) b2 b2 The length of the other side is cm.

NNEL-MATANSWER-08-0702-001-L07.inddEL-MATANSWER-08-0702-001-L07.indd 3300 99/16/08/16/08 11:34:16:34:16 AMAM 6. Fran cycles 6.0 km north along a straight path. She then rides 10.0 km east. Then she rides 3.0 km south. Then she turns and rides in a straight line back to her starting point. What is the total distance of her ride? Solution: The ﬁ rst 3 legs of Fran’s ride have been drawn. Draw the path that takes Fran back to her starting point.

N 10.0 km

WE 3.0 km

6.0 km S

START

Draw a line on the diagram to divide the shape into a rectangle and a right triangle.

Label the hypotenuse Let a short side of Δ b other side of Δ of the triangle c. 6 km km long side of rectangle km. km.

Use the Pythagorean theorem to calculate c. ___ Hint 2 2 2 Ί 2 c a b c _____c 2 2 The original ( ) ( ) Ί measurements are precise to a tenth ᝽ of a centimetre, so round the value of c to the nearest tenth The total distance of Fran’s ride is of a centimetre. 6.0 km 10.0 km 3.0 km km km.

NNEL-MATANSWER-08-0702-001-L07.inddEL-MATANSWER-08-0702-001-L07.indd 3311 99/16/08/16/08 11:34:16:34:16 AMAM Acute triangles Cutout 1.6 (all 3 angles less than 90°)

a = 60 mm b = mm c =mm B A b = 80 mm

c = 80 mm a = 60 mm

Right triangle (1 angle is 90°)

c = mm a = 60 mm

b = 80 mm

Obtuse triangles (1 angle is greater than 90°)

mm c = 80 mm b = 60 mm D 60 mm E

80 mm

a = mm

NNEL-MATANSWER-08-0702-001-L07.inddEL-MATANSWER-08-0702-001-L07.indd 3322 99/16/08/16/08 11:34:16:34:16 AMAM