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.
Solution:
It is given that $\triangle \mathrm{ABC} \sim \triangle \mathrm{DEF}$.
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.
$\Rightarrow \frac{\text { Perimeter of } \triangle A B C}{\text { Perimeter of } \triangle D E F}=\frac{B C}{E F}$
Let the perimeter of ∆ABC be x cm.
Therefore,
$\frac{x}{25}=\frac{9.1}{6.5}$
$\Rightarrow x=\frac{9.1 \times 25}{6.5}=35$
Thus, the perimeter of ∆ABC is 35 cm.