Question

Find CD, if AC = 4 cm, AB = 3 cm and AD = 2 cm.

• A. $\frac{8}{3}cm$
• B. $\frac{3}{8}cm$
• C. $\frac{4}{3}cm$
• D. $\frac{3}{4}cm$

Answer 1

The correct option is A $\frac{8}{3}cm$

Perpendicular from right angle to hypotenuse divides the triangle into two similar triangles and these are similar to the whole triangle also.

$\therefore △CAB\sim △CDA$

$\Rightarrow \frac{AB}{DA}=\frac{CA}{CD}$

$\Rightarrow \frac{3}{2}=\frac{4}{CD}$

$\Rightarrow CD=\frac{8}{3}cm$