Question

The longer leg of a right triangle is 4 more than the short leg. The hypotenuse is eight less than the sum of the 2 legs.

Solve

Please help !

Answer 1

In bold below.

Explanation:

let the shorter leg be x units long, then:

longer leg = x+4

and hypotenuse = x + x + 4 - 8 = 2x - 4 units.

By Pythagoras:

(2x - 4)^2 = x^2 + (x + 4)^2

4x^2 - 16x + 16 = x^2 + x^2 +8x + 16

2x^2 - 24x = 0

2x(x - 12) = 0

x = 12.

So the shorter leg = 12 units

Longer leg = 4 + 12 = 16 units and

Hypotenuse = 12 + 16 - 8 = 20 units.