Question

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 help.

Answer 1

Answer:
Choice B) 8*sqrt(3)

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Step-by-step 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