Question

The shorter leg of a right triangle is 8 Inches than the longer leg. They hypotenuse is 8 inches longer than the long leg. Find the side lengths of the triangle.

Answer 1

Answer:
`24, 32, 40\ in.`

Explanation:

Given

The shorter side is 8 inches shorter than the long side.

The hypotenuse is 8 inches longer than the long side.

Suppose the length of the long side is x

Short side is
`x-8`

hypotenuse is
`x+8`

using Pythagoras theorem

`\Rightarrow \left( x-8\right)^2+\left( x\right)^2=\left( x+8\right)^2\\\Rightarrow x^2+64-16x+x^2=x^2+64+16x\\\Rightarrow x^2-32x=0\\\Rightarrow x\left( x-32\right)=0\\\Rightarrow x=0\ \text{or}\ 32`

Neglecting 0 as length cannot be zero

Shorter side is
`32-8=24\ in.`

long side
`x=32\ in.`

hypotenuse
`32+8=40\ in.`