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Find X. 9. SOLUTION: in a Right Triangle, the Sum of the Squares Of

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Find X. 9. SOLUTION: in a Right Triangle, the Sum of the Squares Of 8-2 The Pythagorean Theorem and Its Converse Find x. 9. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is x and the lengths of the legs are 12 and 16. 10. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is 15 and the lengths of the legs are 9 and x. eSolutions11. Manual - Powered by Cognero Page 1 SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is 5 and the lengths of the legs are 2 and x. 12. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is 66 and the lengths of the legs are 33 and x. 13. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is x and the lengths of the legs are . 14. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is and the lengths of the legs are . Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 21. 7, 15, 21 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle. Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle. 22. 10, 12, 23 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be measures of a triangle. 23. 4.5, 20, 20.5 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle. Classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Therefore, by the converse of Pythagorean Theorem, a triangle with the given measures will be a right triangle. 24. 44, 46, 91 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be measures of a triangle. 25. 4.2, 6.4, 7.6 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle. Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an acute triangle. 26. 4 , 12, 14 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle. Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle. 8-2 The Pythagorean Theorem and Its Converse Find x. 9. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is x and the lengths of the legs are 12 and 16. 10. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is 15 and the lengths of the legs are 9 and x. eSolutions11. Manual - Powered by Cognero Page 2 SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is 5 and the lengths of the legs are 2 and x. 12. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is 66 and the lengths of the legs are 33 and x. 13. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is x and the lengths of the legs are . 14. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is and the lengths of the legs are . Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 21. 7, 15, 21 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle. Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle. 22. 10, 12, 23 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be measures of a triangle. 23. 4.5, 20, 20.5 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle. Classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Therefore, by the converse of Pythagorean Theorem, a triangle with the given measures will be a right triangle. 24. 44, 46, 91 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Since the sum of the lengths of two sides is less than that of the third side, the set of numbers cannot be measures of a triangle. 25. 4.2, 6.4, 7.6 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle. Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an acute triangle. 26. 4 , 12, 14 SOLUTION: By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side. Therefore, the set of numbers can be measures of a triangle. Now, classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. Therefore, by Pythagorean Inequality Theorem, a triangle with the given measures will be an obtuse triangle. 8-2 The Pythagorean Theorem and Its Converse Find x. 9. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is x and the lengths of the legs are 12 and 16. 10. SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The length of the hypotenuse is 15 and the lengths of the legs are 9 and x. eSolutions11. Manual - Powered by Cognero Page 3 SOLUTION: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
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