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Similar Triangles

If Δ ABC ∼Δ P...

Question

If $Δ A B C \sim Δ P Q R$ , and $A B = 6 f t, B C = 10 f t, A C = 12 f t$ and $P Q = 3.6 f t,$ then the value of $Q R + P R$ is.

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Solution

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

Here, vertex $A$ corresponds to vertex $P .$

Given: $A B = 6 f t, B C = 10 f t, A C = 12 f t$ , and $P Q = 3.6 f t .$

So, $\frac{A B}{P Q} = \frac{B C}{Q R} = \frac{A C}{P R}$

$\Rightarrow \frac{6}{3.6} = \frac{10}{Q R} = \frac{12}{P R}$

$\Rightarrow Q R = 6 f t$

And $P R = \frac{9}{2.5} = 7.2 f t$

So, $Q R + P R = 6 + 7.2 = 13.2 f t$

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