Find the value of x

picture attached

x must be 4

Step-by-step explanation:

Write and solve an equation of ratios.  Start with the ratio of the hypotenuses:  

 x + 2         x

=

 x + 5        x + 2

Cross multiplying results in (x + 2)^2 = x^2 + 5x

performing the indicated squaring, (x + 2)^2 = x^2 + 4x + 4.  And therefore:

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

Simplifying, we get 4x + 4 = 5x, so x must be 4

a

step-by-step explanation: