Question

In given figure, (i) and (ii), $PQ||BC$. Find $QC$ in (i) and $AQ$ in (ii).

Answer 1

In figure (i), we have

$PQ||BC$

Therefore, by basic proportionality theorem, we have

$\frac{AP}{PB}=\frac{AQ}{QC}$

$\Rightarrow$ $\frac{1.5}{3}=\frac{1.3}{QC}$

$\Rightarrow$ $\frac{1}{2}=\frac{1.3}{QC}$

$\Rightarrow$ $QC=2.6cm$

In figure (ii), it is given that $PQ||BC$.

Therefore, by basic proportionlity theorem, we have

$\frac{AP}{PB}=\frac{AQ}{QC}$

$\Rightarrow$ $\frac{3}{6}=\frac{AQ}{5.3}$

$\Rightarrow$ $\frac{1}{2}=\frac{AQ}{5.3}$

$\Rightarrow$ $AQ=\frac{5.3}{2}=2.65cm$