Question

The corresponding sides of two similar triangles ABC and DEF are BC = 9.1 cm and EF = 6.5 cm. If the perimeter of ∆ DEF is 25 cm, find the perimeter of ∆ABC.

Answer 1

$\mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}△\mathrm{ABC}~△\mathrm{DEF}.$
Therefore, their corresponding sides will be proportional.
Also, the ratio of the perimeters of similar triangles is same as the ratio of their corresponding sides.

$\Rightarrow \frac{Perimeterof△ABC}{Perimeterof△DEF}=\frac{BC}{EF}$

Let the perimeter of ∆ABC be x cm.

Therefore,
$$\begin{gathered} \frac{x}{25}=\frac{9.1}{6.5} \\ \Rightarrow x=\frac{9.1\times 25}{6.5}=35 \end{gathered}$$

Thus, the perimeter of ∆ABC is 35 cm.