Which of the following measurements could be the side lengths of a right triangle?
A.
√112 in, √48 in, √56 in
B.
√64 in, √16 in, √80 in
C.
√88 in, √16 in, √80 in
D.
√72 in, √48 in, √128 in
B. √64 in, √16 in, √80 in
In a right triangle, the Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, the side lengths must satisfy a^2 + b^2 = c^2, where a and b represent the two shorter sides and c represents the hypotenuse.
For option B:
√64 in = 8 in
√16 in = 4 in
√80 in = 8.944 in
Now we can check:
8^2 + 4^2 = 8.944^2
64 + 16 = 79.9386 (approximately 80)
So, option B could be the side lengths of a right triangle.