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

Given, △ABC ~ △PQR

$\therefore \dfrac{AB}{PQ} = \dfrac{AC}{PR} = \dfrac{BC}{QR} \\[1em]$

Since triangles are similar so the ratio of perimeter will be equal to ratio of sides.

$\Rightarrow \dfrac{\text{Perimeter of △ABC}}{\text{Perimeter of △PQR}} = \dfrac{AC}{PR} \\[1em] \dfrac{32}{48} = \dfrac{AC}{6} \\[1em] AC = \dfrac{192}{48} \\[1em] AC = 4.$

Hence, length of AC = 4 cm.