Question

What is the value of y?

Answer 1

Note that there are 3 triangles here, all similar. Thus, we can write a variety of ratios, and then equations, which in turn can be solved for the unknown side lengths TU and y.

Line MN has length 9+3, or 12. It's the hypotenuse of the large triangle which has legs y and 6. Thus, 12^2 = y^2 + 6^2. Solving for y^2, y^2 = 144 - 36 = 108.

Finally, take the square root of both sides of y^2 = 108, obtaining 6√3.

The length of side y is 6√3.

Answer 2

y^2 = 12^2 - 6^2

y^2 = 144 - 36

y^2 = 108

y = √108

y = √(36 * 3)

y = 6√3

answer

6√3 units