Question

Which of the following measurements could be the side lengths of a right triangle?

A. 132 in, 18 in, 140 in
B. 144 in, 18 in, 140 in
C. 136 in, 524 in, 564 in
D. 156 in, 124 in, 128 in

Answer 1

None of the given sets of measurements could be the side lengths of a right triangle.

Step-by-step explanation:

In order for a set of measurements to represent the side lengths of a right triangle, they must satisfy the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

Let's test each set of measurements:

1. A. 132 in, 18 in, 140 in: The sum of the squares of the two shorter sides is 132^2 + 18^2 = 17484 + 324 = 17808, which is not equal to the square of the longest side (140^2).
2. B. 144 in, 18 in, 140 in: The sum of the squares of the two shorter sides is 144^2 + 18^2 = 20736 + 324 = 21060, which is not equal to the square of the longest side (140^2).
3. C. 136 in, 524 in, 564 in: The sum of the squares of the two shorter sides is 136^2 + 524^2 = 18496 + 274576 = 293072, which is not equal to the square of the longest side (564^2).
4. D. 156 in, 124 in, 128 in: The sum of the squares of the two shorter sides is 156^2 + 124^2 = 24336 + 15376 = 39712, which is not equal to the square of the longest side (128^2).

None of the given sets of measurements satisfy the Pythagorean theorem, so none of them could be the side lengths of a right triangle.