Question : If $\triangle \mathrm{ABC}$ is similar to $\triangle \mathrm{DEF}$ such that $\mathrm{BC}=3 \mathrm{~cm}, \mathrm{EF}=4 \mathrm{~cm}$ and the area of $\triangle \mathrm{ABC}=54 \mathrm{~cm}^2$, then the area of $\triangle \mathrm{DEF}$ is:
Option 1: 78 cm2
Option 2: 96 cm2
Option 3: 66 cm2
Option 4: 44 cm2
Correct Answer: 96 cm 2
Solution :
Given,
$\triangle \mathrm{ABC}\sim \triangle \mathrm{DEF}$
$\mathrm{BC}=3 \mathrm{~cm}, \mathrm{EF}=4 \mathrm{~cm}$ and the area of $\triangle \mathrm{ABC}=54 \mathrm{~cm}^2$
⇒ $\frac{area(\triangle{ABC})}{area(\triangle{DEF})}=\frac{BC^2}{EF^2}$
⇒ $\frac{54}{area(\triangle{DEF})}=\frac{3^2}{4^2}$
⇒ $\frac{54}{area(\triangle{DEF})}=\frac{9}{16}$
⇒ $area(\triangle{DEF})=\frac{54\times16}{9}$
⇒ $area(\triangle{DEF})=96$ cm$^2$
Hence, the correct answer is 96 cm$^2$
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