Question

The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. find the lengths of the three sides of the triangle.

Answer 1

suppose the shortest leg is x, the hypotenuse is then 3x-8, and the longer leg is 2x+8
use the pythagorean theorem:
x^2+(2x+8)^2=(3x-8)^2
x^2+(4x^2+32x+64)=(9x^2-48x+64)
4x^2-80x=0
x=0 or x=20
so the sides are 20, 48, and 52

Answer 2

The sides of the right angle triangle are 20, 48, and 52.

We have given that,

The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg.

Suppose the shortest leg is x, the hypotenuse is then 3x-8, and the longer leg is 2x+8

We use the Pythagorean theorem

What is the Pythagorean theorem?

$hypotenous^2=side^2+side^2$

Therefore by using Pythagorean theorem

$x^2+(2x+8)^2=(3x-8)^2\\x^2+(4x^2+32x+64)=(9x^2-48x+64)\\4x^2-80x=0$

x=0 or x=20

So the sides are 20, 48, and 52.

To learn more about the Pythagorean theorem visit:

https://brainly.com/question/343682

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