Question

Find the value of y. 4 2 √3 6 6 √3

Answer 1

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