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

The length of the hypotenuse is 26 ft.

Let x be the length of the shorter leg.

The length of the hypotenuse is x + 16 ft.

The area of the triangle is (1/2)(x)(x + 16) = 120 ft^2.

Simplifying the equation, we get (x^2 + 16x) = 240.

Rearranging the equation, we get x^2 + 16x - 240 = 0.

Factoring the equation, we get (x - 10)(x + 24) = 0.

Since x cannot be negative, x = 10.

Therefore, the length of the hypotenuse is 10 + 16 = 26 ft.