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Which of the following sets of measurements will give the sides of a right angle triangle and why A. 5,8,10 B. 7,24,30 C. 8,16,16 D. 5,12,13?
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Which of the following sets of measurements will give the sides of a r...
Answer:
Introduction:
In order for a set of measurements to represent the sides of a right-angled triangle, they must satisfy the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Analysis of the options:
Option A: 5, 8, 10
- The square of the length of the hypotenuse is 10^2 = 100.
- The sum of the squares of the lengths of the other two sides is 5^2 + 8^2 = 25 + 64 = 89.
- Since the square of the hypotenuse is not equal to the sum of the squares of the other two sides, option A does not represent the sides of a right-angled triangle.
Option B: 7, 24, 30
- The square of the length of the hypotenuse is 30^2 = 900.
- The sum of the squares of the lengths of the other two sides is 7^2 + 24^2 = 49 + 576 = 625.
- Since the square of the hypotenuse is equal to the sum of the squares of the other two sides, option B represents the sides of a right-angled triangle.
Option C: 8, 16, 16
- The square of the length of the hypotenuse is 16^2 = 256.
- The sum of the squares of the lengths of the other two sides is 8^2 + 16^2 = 64 + 256 = 320.
- Since the square of the hypotenuse is not equal to the sum of the squares of the other two sides, option C does not represent the sides of a right-angled triangle.
Option D: 5, 12, 13
- The square of the length of the hypotenuse is 13^2 = 169.
- The sum of the squares of the lengths of the other two sides is 5^2 + 12^2 = 25 + 144 = 169.
- Since the square of the hypotenuse is equal to the sum of the squares of the other two sides, option D represents the sides of a right-angled triangle.
Conclusion:
Out of the given options, only option B (7, 24, 30) and option D (5, 12, 13) represent the sides of a right-angled triangle. These options satisfy the Pythagorean theorem, where the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Introduction:
In order for a set of measurements to represent the sides of a right-angled triangle, they must satisfy the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Analysis of the options:
Option A: 5, 8, 10
- The square of the length of the hypotenuse is 10^2 = 100.
- The sum of the squares of the lengths of the other two sides is 5^2 + 8^2 = 25 + 64 = 89.
- Since the square of the hypotenuse is not equal to the sum of the squares of the other two sides, option A does not represent the sides of a right-angled triangle.
Option B: 7, 24, 30
- The square of the length of the hypotenuse is 30^2 = 900.
- The sum of the squares of the lengths of the other two sides is 7^2 + 24^2 = 49 + 576 = 625.
- Since the square of the hypotenuse is equal to the sum of the squares of the other two sides, option B represents the sides of a right-angled triangle.
Option C: 8, 16, 16
- The square of the length of the hypotenuse is 16^2 = 256.
- The sum of the squares of the lengths of the other two sides is 8^2 + 16^2 = 64 + 256 = 320.
- Since the square of the hypotenuse is not equal to the sum of the squares of the other two sides, option C does not represent the sides of a right-angled triangle.
Option D: 5, 12, 13
- The square of the length of the hypotenuse is 13^2 = 169.
- The sum of the squares of the lengths of the other two sides is 5^2 + 12^2 = 25 + 144 = 169.
- Since the square of the hypotenuse is equal to the sum of the squares of the other two sides, option D represents the sides of a right-angled triangle.
Conclusion:
Out of the given options, only option B (7, 24, 30) and option D (5, 12, 13) represent the sides of a right-angled triangle. These options satisfy the Pythagorean theorem, where the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Community Answer
Which of the following sets of measurements will give the sides of a r...
Correct answer is option c because the right angle triangle is isosceles triangle means it have two sides same in option c the 16 and 16 are same so the correct answer is c
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Which of the following sets of measurements will give the sides of a right angle triangle and why A. 5,8,10 B. 7,24,30 C. 8,16,16 D. 5,12,13?
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Which of the following sets of measurements will give the sides of a right angle triangle and why A. 5,8,10 B. 7,24,30 C. 8,16,16 D. 5,12,13? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Which of the following sets of measurements will give the sides of a right angle triangle and why A. 5,8,10 B. 7,24,30 C. 8,16,16 D. 5,12,13? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following sets of measurements will give the sides of a right angle triangle and why A. 5,8,10 B. 7,24,30 C. 8,16,16 D. 5,12,13?.
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