Question

In the figure, $RS\parallel DB\parallel PQ.$ If $CP=PD=11cm$ and $DR=RA=3cm.$ Then the values of $x,y$ and $z$ can be

• A. $12,10,12$
• B. $14,6,6$
• C. $10,7,10$
• D. $16,8,8$

Answer 1

The correct option is D $16,8,8$

Given $RS\parallel DB\parallel PQ$

$\Rightarrow CP=PD=11cm$

$\Rightarrow DR=RA=3cm$

To find $x,y$ and $z$

In $△ASR$ and $△ABD$

$\angle ASR=\angle ABD$ ( corresponding angles )

$\angle A=\angle A$ ( common )

$\therefore △ASR\sim △ABD$ ( AA similarity )

$\Rightarrow \frac{AR}{AD}=\frac{AS}{AB}=\frac{RS}{DB}$ ( CPST )

$\Rightarrow \frac{AR}{AD}=\frac{RS}{DB}$

$\Rightarrow \frac{AR}{DR+RA}=\frac{RS}{DB}$

$\Rightarrow \frac{3}{6}=\frac{RS}{DB}$

$\Rightarrow \frac{1}{2}=\frac{y}{x}$

$\Rightarrow x=2y$

This relation is satisfied when $x=16,y=8$ and $z=8$

Hence, the answer is $16,8,8.$