Question

In a $\Delta ABC,$ the sides $AB,BC$ and $CA$ are $10cm,8cm$ and $7cm$ respectively. On $AB,$ a point $P$ is taken such that $AP=4cm.$ If $PQ$ is drawn parallel to $BC,$ then its length is equal to:

• A. $4.0cm$
• B. $3.8cm$
• C. $3.5cm$
• D. $3.2cm$

Answer 1

The correct option is D $3.2cm$

Since $PQ\parallel BC$, $\frac{AP}{PB}=\frac{AQ}{QC}$ ...Basic Proportionality Theorem

In $△APQ$ and $△ABC$

$\angle A$ is common angle.

$\angle APQ=\angle ABC$ ....Corresponding angles since $PQ||BC$

$\therefore △APQ\sim △ABC$ ....AA test of similarity

$\frac{AP}{AB}=\frac{AQ}{AC}=\frac{PQ}{BC}$ ....C.S.S.T

$\frac{4}{10}=\frac{PQ}{8}$.........(On substituting the values)

$PQ=3.2$cm.