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.
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.
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