Question

Choose the option that best answers the question. The hypotenuse of a right triangle is 16 ft longer than the length of the shorter leg. If the area of this triangle is exactly 120 ft2, what is the length of the hypotenuse in feet?

Answer 1

Answer: The hypotenuse is 26 ft.

Step-by-step explanation: Let's call the shorter leg of the triangle x. The hypotenuse would be x + 16 and the other leg is y.

As the area is 120, we know that x.y/2 = 120 (because it's a right triangle).

This way, y = 240/x

we know that in a right triangle, we have a² = b² + c²

(x + 16)² = x² + y²

(x + 16)² = x² + (240/2)²

x² + 32x + 256 = x² + 57600/x²

32x + 256 = 57600/x²

32x³ + 256x² = 57600 (÷ 32)

x³ + 8x² = 1800

x = 10

∴

x + 16 = 26

y = 240/10 = 24