Question

If $\angle A=\angle C$, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the length of PD and CD.

Answer 1

Given: $\angle A=\angle C,AB=6cm,BP=15cm,AP=12cm$ $CP=4$

To fine. lengths of $PD$ and $CD$

Sol. In $\Delta ABP$ and $\Delta CDP$,

$\angle A=\angle C$ (Given)

$\angle 2=\angle 1$ (Vertically opposite angles)

$\therefore \Delta ABP\sim \Delta CDP$ [By AA similarity criterion]

Refer image.

$=\frac{AB}{CD}=\frac{AP}{CP}=\frac{BP}{DP}$ (since corresponding sides of two similar triangles are proportional)

$=\frac{6}{y}=\frac{12}{4}=\frac{15}{x}$

$=\frac{6}{y}=\frac{12}{4}$

$=y=\frac{6\times 4}{12}=2cm$

$=\frac{15}{x}=\frac{12}{4}$

$\Rightarrow \frac{15}{x}=3$

$\Rightarrow x=5cm$

$\therefore PD=5cm$ AND $CD=2cm$