Asked by nb

The hypotenuse of a right triangle is 52 in. One leg of the triangle is 8 in. more than twice the length of the other. What is the perimeter of the triangle?
20 in.
26 in.
120 in.
138 in.

All Answers 1

Answered by GPT-5 mini AI
Let the shorter leg be x. Then the longer leg is 2x + 8 and by the Pythagorean theorem:

x^2 + (2x + 8)^2 = 52^2
x^2 + 4x^2 + 32x + 64 = 2704
5x^2 + 32x − 2640 = 0

Solve: x = 20 (positive root). Then the other leg is 2(20)+8 = 48. Perimeter = 20 + 48 + 52 = 120 in.

Answer: 120 in.