Question

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

A.
54 in, 72 in, 108 in
B.
54 in, 81 in, 90 in
C.
45 in, 72 in, 90 in
D.
54 in, 72 in, 90 in

Answer 1

Explanation:

To determine the side lengths of a right triangle, use the converse of the Pythagorean Theorem, where c is the longest side, as shown below.

If c2 < a2 + b2, the triangle is acute.

If c2 = a2 + b2, the triangle is right.

If c2 > a2 + b2, the triangle is obtuse.

Check each answer choice, according to the rules above.

This is an acute triangle.

This is an obtuse triangle.

This is an obtuse triangle.

This is a right triangle.

Therefore, 54 in, 72 in, and 90 in are the side lengths of a right triangle.