What is the value of y? (confused, geometry)

a. 3√3
b.6√3
c.9√3
d.12√3

Y^2 = 12^2 - 6^2
y^2 = 144 - 36
y^2 = 108
y = 6√3

answer is B.6√3

We can use pythagorean theorem to solve this ... since we have a and c, we can use c^2 - a^2 = b^2

12^2 - 6^2 = b^2
144 - 36 = b^2
180 = b^2            (now we get the square root of each side)
√108 = √b²          (108 can be written as 36 times 3)
√36 √3 = √b²
6√3 = b

so, your answer is 6√3...B