Find the value of x.
a. 4 square root of 3
b. 8 square root of 3
c. 8
d. 16

i feel like it may be c but my gut says ask for some .

 
Choice B) 8*sqrt(3)



Explanation:

First we need to find y
It turns out we can set up the proportion 
4/y = y/12
since the two inner smaller triangles are similar triangles

Solve for y by cross multiplying
4/y = y/12
4*12 = y*y
48 = y^2
y^2 = 48
y = sqrt(48)

Now use this y value to find x
Use the pythagorean theorem. Focus on the smaller triangle on the right side
a^2 + b^2 = c^2
y^2 + 12^2 = x^2
(sqrt(48))^2 + 12^2 = x^2
48 + 144 = x^2
192 = x^2
x^2 = 192
x = sqrt(192)
x = sqrt(64*3)
x = sqrt(64)*sqrt(3)
x = 8*sqrt(3)

So that's why the answer is choice B