Question

Find the value of y.

4

2 √3

6

6 √3

Answer 1

`\triangle ABC\ \text{and}\ \triangle ACD\ \text{are similar. Therefore the sides of triangles}\\\text{ are in proportion:}\\\\(y)/(9+3)=(9)/(y)\qquad\text{cross multiply}\\\\y^2=(9)(12)\\\\y^2=108\to y=√(108)\\\\y=√(36\cdot3)\\\\y=√(36)\cdot\sqrt3\\\\\boxed{y=6\sqrt3}`