Question

In a $△ABC,P$ and $Q$ are the points on sides $AB$ and $BC$ respectively, such that $PQ\parallel BC$. Also, $AP=2cm,PB=4cm,AQ=3cm$ and $QC=6cm$ then find $BC$

• A. $PQ$
• B. $2PQ$
• C. $3PQ$
• D. $4PQ$

Answer 1

Answer: (C)

$3PQ$

Let $ABC$ be a triangle. Let $P,Q$ are the points on sides $AB,BC$ respectively such that $PQ||BC$.

Given $AP=2cm,PB=4cm,AQ=3cm,QC=6cm$.

We have to find $BC$.

The pictorial representation of the problem is shown below

Since we have $PQ||BC$ we get $\Delta APQ\sim \Delta ABC$ by AAA

$\Rightarrow \frac{AP}{AB}=\frac{AQ}{AC}=\frac{PQ}{BC}$

Substituting the values we get,

$\Rightarrow \frac{2}{6}=\frac{3}{9}=\frac{PQ}{BC}$

$\Rightarrow \frac{1}{3}=\frac{1}{3}=\frac{PQ}{BC}$

$\Rightarrow \frac{1}{3}=\frac{PQ}{BC}$

$\Rightarrow BC=3PQ$