Question

What are the values of $x$ and $y$ if $△ABC~△PQR$ ?

• A. $y=3\text{and}x=\frac{1}{3}$
• B. $x=3\text{and}y=\frac{1}{3}$
• C. $x=3\text{and}y=3$
• D. $x=\frac{1}{3}\text{and}y=\frac{1}{3}$

Answer 1

The correct option is B $x=3\text{and}y=\frac{1}{3}$

The given figure is as follows:


As $△ABC~△PQR$
So,
$\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}(\because \text{similar triangles have corresponding sides in proportion})$

So, $\frac{10}{5}=\frac{3y+5}{3}$
$\Rightarrow 6=3y+5$
$\Rightarrow 3y=1$
$\Rightarrow y=\frac{1}{3}$

Similarly, $\frac{10}{5}=\frac{20}{2x+4}$
$\Rightarrow 2=\frac{20}{2x+4}$
$\Rightarrow 2x+4=10$
$\Rightarrow 2x=6$
$\Rightarrow x=3$

Hence, option $\left(b\right)$ is correct.