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:

Please see the attachment

Answer 2

The length of hypotenuse =(10+16)ft=26ft.

Step-by-step explanation:

Given, the hypotenuse  of right triangle is 16 ft longer than of the shorter leg.

The area of this triangle is 120 ft²

Let the length of shorter leg x.

Then the length of hypotenuse is (x+16)

We know that

base²+ height²=hypotenuse²

⇔x²+height²=(x+16)²

⇔height²= 32x+256

⇔height =$\sqrt{32x+256}$

According to question

$\frac{1}{2} \times x\times \sqrt{32x+256}=120$

⇔x²(32x+256)=240²

⇔32x³+256x²-57600=0

⇔x³+8x²-1800=0

⇔x³-10x²+18x²-180x+180x-1800=0

⇔ x²(x-10)+18x(x-10)+180(x-10)=0

⇔(x-10)(x²+18x+180)=0

Therefore x= 10

The length of hypotenuse =(10+16)ft=26ft.