Answer: x = 4
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Step-by-step explanation
Let y be the height
We have three right triangles that are all similar. We can form the proportion below to solve for y^2. We don't have to find the value of y itself.
2/y = y/6
2*6 = y*y
12 = y^2
y^2 = 12
Now focus on the smaller triangle on the left. It has legs of 2 and y with hypotenuse x
Use the pythagorean theorem to find x
a^2+b^2 = c^2
2^2+y^2 = x^2
4 + 12 = x^2
x^2 = 16
x = sqrt(16)
x = 4