Question

In the figure, $AC=10cm,PC=15cm,PQ=12cm,$ find PB.

• A. $6cm$
• B. $7cm$
• C. $8cm$
• D. $9cm$

Answer 1

The correct option is D

$9cm$

In $\Delta ABC$ and $\Delta PQC,$
$\angle PQC=\angle ABC={90}^{\circ }$
$\angle C=\angle C$ [common angle]
Therefore, $\Delta ABC\sim \Delta PQC$ [AA similarity]
$\frac{AC}{PC}=\frac{AB}{PQ}=\frac{BC}{QC}\Rightarrow \frac{10}{15}=\frac{AB}{12}=\frac{BC}{QC}$
$\Rightarrow AB=8cm$
In $\Delta ABC,$
$A{B}^2+B{C}^2=A{C}^2\Rightarrow {10}^2=8^2+B{C}^2\Rightarrow BC=6cm$
$PB=PC-BC=15-6=9cm$
Hence, $PB=9cm.$