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

answer: 16

step-by-step explanation: first you would add 6+6 which equals 12 then add 2+2 which equals 4. then add 12 + 4 which is 16.

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