Question

The length of the longer leg of a right triangle is 20 cm more than twice the length of the shorter leg. The length of the hypotenuse is 22 cm more than twice the length of the shorter leg. Find the side lengths of the triangle.

Answer 1

the answer is 14 cm. the solution is just like in the photo

Answer 2

Hi,

Explanation:

Let's say x the length of the shorter leg:

Using the Pytagorean's theorem:

`(20+2x)^2+x^2=(22+2x)^2\\4x^2+80x+400+x^2=4x^2+88x+484\\x^2-8x-84=0\\\Delta=8^2+4*84=400=20^2\\\\x=(8+20)/(2) =14\ or\ x=(8-20)/(2) =-6\ (impossible)\\`

shorter leg =14

longer leg= 20+2*14=48

hypotenuse=22+2*14=50

Proof: 14²+48²=2500=50²