Question

In the given figure, $△ABC$ and $△DEF$ are similar. If BC = 3 cm, EF = 4 cm and area of $△ABC$ is 54 cm${}^2$, then the area of $△DEF$ is _____ cm${}^2$.

• A. 96
• B. 48
• C. 24
• D. 64

Answer 1

The correct option is A 96

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

$\Rightarrow \frac{ar\left(△ABC\right)}{ar\left(△DEF\right)}=\frac{B{C}^2}{E{F}^2}$

$\Rightarrow \frac{54}{Ar\left(△DEF\right)}=(\frac{3}{4}{)}^2$

$\Rightarrow Ar\left(△DEF\right)=\frac{54\times 16}{9}$

$\therefore \text{Area of}△DEF=96c{m}^2$