If $△ A B C ~ △ P Q R$ , and $A B = 4 c m, B C = 8 c m, A C = 9 c m$ and $P Q = 1.6 c m,$ find the value of $Q R + P R$ .

6

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6.4

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6.8

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3.2

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Solution

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: $A B = 4 c m, B C = 8 c m, A C = 9 c m$ and $P Q = 1.6 c m .$

So, $\frac{A B}{P Q} = \frac{B C}{Q R} = \frac{A C}{P R}$
$\Rightarrow \frac{4}{1.6} = \frac{8}{Q R} = \frac{9}{P R}$
$\Rightarrow Q R = 3.2 c m$
And, $P R = \frac{9}{2.5} = 3.6 c m$
So, $Q R + P R = 3.2 + 3.6 = 6.8 c m$

Hence, option $(c)$ is correct.

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