Question : If $\triangle A B C \sim \triangle D E F$, and $B C=4 \mathrm{~cm}, E F=5 \mathrm{~cm}$ and the area of triangle $A B C=80 \mathrm{~cm}^2$, then the area of the $\triangle DEF$ is:
Option 1: 169 cm2
Option 2: 80 cm2
Option 3: 144 cm2
Option 4: 125 cm2
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Correct Answer: 125 cm 2
Solution :
$\triangle$ ABC ~ $\triangle$ DEF, hence the ratio of areas of two similar triangles is equal to the ratio of the square of their corresponding sides.
$\frac{\text{area of }(\triangle ABC)}{\text{area}(\triangle DEF)}=\frac{BC^{2}}{EF^{2}}$
$⇒\frac{80}{\text{area of}(\triangle DEF)}=\frac{4^{2}}{5^{2}}$
$⇒\frac{80}{\text{area of}(\triangle DEF)}=\frac{16}{25}$
$⇒\text{area of}(\triangle DEF) = \frac{80 \times 25}{16}$
$⇒\text{area of}(\triangle DEF) = 125$ cm
2
Hence, the correct answer is 125 cm
2
.
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