Question

Using the pythagorean theorem how do you find the unknown lengths A=5x-1 B=x+2 C=5x?

Answer 1

Two solutions. The three lengths are either `3, 4 and 5` or `7, 24 and 25`.

Explanation:

It is apparent in three sides of right angled triangle (as Pythagorean theorem is indicated) that among three sides `A=5x-1`, `B=x+2` and `C=5x`, `C` is the largest. Applying Pythagoras theorem,

`(5x-1)^2+(x+2)^2=5x^2` or

`25x^2-10x+1+x^2+4x+4=25x^2` or

`x^2-6x+5=0`. Factorizing this, we get

`(x-5)(x-1)=0` or `x=5 or 1`

Putting `x=5`, the three lengths are `24, 7, 25`

and putting `x=1`, the three lengths are `4, 3, 5`