Question

∆ ABC ∼ ∆ PQR and the perimeters of ∆ ABC and ∆ PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, find AB.

Answer 1

We know that the ratio of perimeters of two similar triangles is same as the ratio of their corresponding sides.
Therefore,
$$\begin{gathered} \frac{\mathrm{Perimeter}\mathrm{of}△ABC}{\mathrm{Perimeter}\mathrm{of}△PQR}=\frac{AB}{PQ} \\ \mathrm{Let}AB\mathrm{be}xcm. \\ \Rightarrow \frac{36}{24}=\frac{x}{10} \end{gathered}$$

$\Rightarrow x=\frac{360}{24}=15$

Hence, AB = 15 cm