Question

The perimeters of two similar triangles ABC and PQR are 32 cm and 24 cm respectively. If PQ = 12 cm, find AB.

Answer 1

$\Delta ABC\sim \Delta PQR$

$\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}=\frac{AB+BC+AC}{PQ+QR+PR}$ (Corresponding sides are proportional)

$\Rightarrow \frac{AB+BC+AC}{PQ+QR+PR}=\frac{AB}{PQ}$

$\Rightarrow \frac{\text{Perimeter of ABC}}{\text{Perimeter of PQR}}=\frac{AB}{PQ}$

$\Rightarrow \frac{32}{24}=\frac{AB}{12}$

$\Rightarrow AB=\frac{32}{24}\times 12=16$