Question

Find x.

A) 2√5

B) 3√5

C) 6

Answer 1

Look at the picture.

ΔABC and ΔDAC are similar. Therefore the sides of the triangles are in proportion:

$\dfrac{AC}{BC}=\dfrac{DC}{AC}$

AC = x

BC = 5 + 4 = 9

DC = 4

Substitute:

$\dfrac{x}{9}=\dfrac{4}{x}$          cross multiply

$x^2=(9)(4)\\\\x^2=36\to x=\sqrt{36}\\\\\boxed{x=6\to C)}$