Question

Triangle $ABC$ is such that $AB=3cm,BC=2cm$ and $CA=2.5cm$. Triangle $DEF$ is similar to $△ABC$. If $EF=4cm$, then the perimeter of $△DEF$ is:

• A. $7.5cm$
• B. $15cm$
• C. $22.5cm$
• D. $30cm$

Answer 1

In $\Delta ABC$,

$AB=3cm,BC=2cm$ and $CA=2.5cm$

$△ABC\sim △DEF$

So, the corresponding sides are in the same ratio.

$\Rightarrow \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

$\Rightarrow \frac{3}{DE}=\frac{2}{4}=\frac{2.5}{DF}$
Thus,

$\Rightarrow \frac{3}{DE}=\frac{2}{4}$

$\Rightarrow DE=\frac{4\times 3}{2}=6$

Similarly,

$\frac{2.5}{DF}=\frac{2}{4}$

$\Rightarrow DF=\frac{4\times 2.5}{2}=5$

Now, Perimeter of $△DEF=DE+FE+DF$

$=(6+4+5)cm$

$=15cm$

The correct option is B $15cm$.