Question

Find the value of $x,$ if $△ABC\sim △PQR.$

• A. $2$ unit
• B. $4$ unit
• C. $6$ unit
• D. $8$ unit

Answer 1

The correct option is B $4$ unit

$\text{Given:}$
$\bullet$ $△ABC\sim △PQR$
$\bullet BC=4$
$\bullet CA=x$
$\bullet QR=8$
$\bullet RP=8$


We know that the corresponding sides of similar triangles are proportional.

$\therefore$ $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CA}{RP}$
$\Rightarrow \frac{BC}{QR}=\frac{CA}{RP}$
$\Rightarrow \frac{4}{8}=\frac{x}{8}$
Multiplying both sides by $8$,
$\Rightarrow \frac{4}{8}\times 8=\frac{x}{8}\times 8$
$\Rightarrow 4=x$

Hence, value of $x$ is $4$ unit.

So, option (b.) is correct.