Question

Find the value of x​

Answer 1

The larger right triangle with hypotenuse x + 5 and short leg x + 2 is similar to the smaller right triangle with hypotenuse x + 2 and short leg x.

Because of this similarity, we have

(x + 5)/(x + 2) = (x + 2)/x

Solve for x:

x(x + 5) = (x + 2)^2

x^2 + 5x = x^2 + 4x + 4

x = 4