Question

If $△ABC~△PQR$, and $AB=4cm,BC=8cm,AC=9cm$ and $PQ=1.6cm,$ find the value of $QR+PR$.

• A. $6$ cm
• B. $6.4$ cm
• C. $6.8$ cm
• D. $3.2$ cm

Answer 1

The correct option is C $6.8$ cm

As the triangles are similar, so their corresponding sides are in the same ratio.

Here, vertex $A$ corresponds to vertex $P.$
Given: $AB=4cm,BC=8cm,AC=9cm$ and $PQ=1.6cm.$

So, $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$
$\Rightarrow \frac{4}{1.6}=\frac{8}{QR}=\frac{9}{PR}$
$\Rightarrow QR=3.2cm$
And, $PR=\frac{9}{2.5}=3.6cm$
So, $QR+PR=3.2+3.6=6.8cm$

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