Question

solve for y

A. 8

B.
$3 \sqrt{7}$
C.
$4 \sqrt{7}$
D. 12

Answer 1

Triangle ADC and triangle BCD are similar, therefore the sides are in proportion:

$\dfrac{y}{9}=\dfrac{7}{y}$

cross multiply

$y^2=9\cdot7\to y=\sqrt{9\cdot7}\\\\y=\sqrt9\cdot\sqrt7\\\\y=3\sqrt7$

Answer: B. 3√7