Question

Question 1
In given figure, if $\angle A=\angle C$, AB = 6cm, BP = 15cm, AP = 12cm and CP = 4cm, then find the lengths of PD and CD.

Answer 1

Given, $\angle A=\angle C,AB=6cm,BP=15cm,AP=12cm$ and $CP=4cm$
In $\Delta APB$ and $\Delta CPD$,
$\angle A=\angle C$ [given]
$\angle APB=\angle CPD$ [vertically opposite angles]
$\therefore$ $\Delta APB\sim \Delta CPD$ [ by AAA similarity criterion]
$\Rightarrow \frac{AP}{CP}=\frac{PB}{PD}=\frac{AB}{CD}$
$\Rightarrow \frac{12}{4}=\frac{15}{PD}=\frac{6}{CD}$
On taking first and second term, we get
$\frac{12}{4}=\frac{15}{PD}$
$\Rightarrow PD=\frac{15\times 4}{12}=5cm$
On taking first and last term, we get
$\frac{12}{4}=\frac{6}{CD}$
$\Rightarrow CD=\frac{6\times 4}{12}=2cm$
Hence, length of PD = 5 cm and length of CD = 2 cm