The triangle shown is a right triangle having sides a, b, and c. Given that the measurements of a = 12 cm, b = 16 cm, and c = 20 cm, which of these statements is true?

Question

A. The sum of the squares of the 2 smaller sides is equal to the third side.
B. The sum of the 2 smaller sides is equal to the third side.
C. The sum of the squares of the 2 smaller sides is equal to the square of the third side.
D. The absolute value of the difference between the squares of the 2 smaller sides is equal to square of the third side.

Answer 1

C. The sum of the squares of the 2 smaller sides is equal to the square of the third side.

This is the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In this case, a = 12 cm, b = 16 cm, and c = 20 cm, so 12^2 + 16^2 = 20^2, which is true.