The corresponding sides of two similar triangles ABC and DEF are BC = 9.1 cm and EF = 6.5 cm.


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.


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.



$\Rightarrow x=\frac{9.1 \times 25}{6.5}=35$

Thus, the perimeter of ∆ABC is 35 cm.



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