Answer:
x = 8
Explanation:
In this geometry, all of the triangles are similar right triangles. That means corresponding sides are proportional. The proportion you write will express that relation for the sides you are given.
long side / short side = x/4 = 4/(x-6)
Multiplying this proportion by 4(x-6) gives ...
x(x -6) = 16
We can add 9 to complete the square.
x^2 -6x +9 = 16 +9
(x -3)^2 = 25
x -3 = 5 . . . . . . . take the square root (only the positive root is of interest)
x = 8 . . . . . . . . . add 3