Question

If $△ABC\sim △PQR$, Perimeter of $△ABC=32cm$, perimeter of $△PQR=48cm$ and $PR=6cm$, then find the length of $AC$.

Answer 1

From the question it is given that,

$△ABC\sim △PQR$

Perimeter of $△ABC=32cm$

Perimeter of $△PQR=48cm$

So, $\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$

Then, $\frac{\text{perimeter of}△ABC}{\text{perimeter of}△PQR}=\frac{AC}{PR}$

$\frac{32}{48}=\frac{AC}{6}$

$AC=\frac{(32\times 6)}{48}$

$AC=4$

Therefore, the length of $AC=4cm$.