Question

The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 10 cm, find AB.

Answer 1

Since the ratio of the corresponding sides of similar triangles is same as the ratio of their perimeters.

$\therefore$ $△$ABC ~ $△$PQR

$\Rightarrow$ $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}=\frac{36}{24}$

$\Rightarrow$ $\frac{AB}{PQ}=\frac{36}{24}$

$\Rightarrow$ $\frac{AB}{10}=\frac{36}{24}$

$\Rightarrow$ AB = $\frac{36\times 10}{24}$ cm = 15 cm