Question

Solve For Z

A. 12

B.
$4 \sqrt{7}$
C.
$3 \sqrt{7}$
D. 51

Answer 1

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

$\dfrac{z}{9+7}=\dfrac{7}{z}$

cross multiply

$z^2=16\cdot7\to z=\sqrt{16\cdot7}\\\\z=\sqrt{16}\cdot\sqrt7\\\\z=4\sqrt7$

Answer: B. 4√7