# In a triangle ABC, angle ABC = 90 and BD is perpendicular to AC. If BD = 8 cm and AD = 4 cm then find the length of CD?

Feb 1, 2017

$C D = 16$ cm

#### Explanation:

Given $\angle A B C = {90}^{\circ} , B D$ is perpendicular to $A C$, $B D = 8 , \mathmr{and} A D = 4$, as shown in the diagram.
Let $\angle A C B = x , \implies \angle C B D = 90 - x$
$\implies \angle A B D = x , \implies \angle B A D = 90 - x$
$\implies \Delta A B C , \Delta A D B , \mathmr{and} \Delta B D C$ are similar

$\implies \frac{B D}{C D} = \frac{A D}{D B}$
$\implies \frac{8}{C D} = \frac{4}{8}$
$\implies C D = \frac{8 \times 8}{4} = 16$