Question

Solve for X

A: 12.5
B: 5
C: 6$\sqrt{3}$
D:12

Answer 1

Answer:

D. 12

Step-by-step explanation:

(LOOK AT THE PICTURE)

ΔADC and ΔCDB are similar (AAA). Therefore the corresponding sides are in proportion:

$\dfrac{AD}{CD}=\dfrac{CD}{DB}$

We have

$AD=16,\ CD=x,\ DB=9$

Substitute:

$\dfrac{16}{x}=\dfrac{x}{9}$          cross multiply

$x^2=(9)(16)\to x=\sqrt{(9)(16)}\\\\x=(\sqrt9)(\sqrt{16})\\\\x=(3)(4)\\\\x=12$

Answer 2

bear in mind that, a perpendicular line stemming from the right-angle like so, creates three similar triangles, a large one, containing the other two smaller ones, a medium and a small.

so.. .we can just use the medium and small proportions.

Check the picture below.