Question

In $\Delta ABC$,$AB=5$, $BC=6$, $AC=7$, $\Delta PQR-\Delta ABC$. Perimeter of $\Delta PQR$ is $360$. Find PQ, QR and PR.

Answer 1

Given, $△ABC\sim △PQR$, as corresponding sides of similar triangles are proportional,

$\therefore \frac{AB}{PQ}=\frac{BC}{QR}=\frac{CA}{RP}=\frac{1}{k}$(let)

Also, $AB=5,BC=6,AC=7$ So, $PQ=5k,QR=6k,RP=7k$

Perimeter of $△PQR=PQ+QR+RP$

$\Rightarrow 360=5k+6k+7k\Rightarrow 360=18k\Rightarrow k=20$

Thus, $PQ=5\times 20=100,QR=6\times 20=120,RP=7\times 20=140$