Answer:
A. 24 in, 32 in, 40 in
Explanation:
To determine whether a set of measurements could be the side lengths of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides.
Using this theorem, we can check each set of measurements:
A. 24 in, 32 in, 40 in
Here, 40 in is the longest side, so it could be the hypotenuse. If we square the other two sides and add them together, we get:
24^2 + 32^2 = 576 + 1024 = 1600
And if we square the length of the hypotenuse, we get:
40^2 = 1600
So this set of measurements satisfies the Pythagorean theorem and could be the side lengths of a right triangle.
B. 24 in, 36 in, 40 in
Again, 40 in is the longest side and could be the hypotenuse. Squaring and adding the other two sides gives:
24^2 + 36^2 = 576 + 1296 = 1872
And squaring the length of the hypotenuse gives:
40^2 = 1600
So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.
C. 24 in, 32 in, 48 in
Here, again, we can take 48 in as the hypotenuse. Squaring and adding the other two sides gives:
24^2 + 32^2 = 576 + 1024 = 1600
And squaring the length of the hypotenuse gives:
48^2 = 2304
So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.
D. 20 in, 32 in, 40 in
Once more, we can take 40 in as the hypotenuse. Squaring and adding the other two sides gives:
20^2 + 32^2 = 400 + 1024 = 1424
And squaring the length of the hypotenuse gives:
40^2 = 1600
So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.
In conclusion:
A set of measurements that could be side lengths of a right triangle is A) {24in,32in,40in}. The other sets do not satisfy Pythagorean theorem and cannot be sides of a right triangle.