Question : $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are similar triangles and their areas are 49 cm2 and 144 cm2 respectively, If $EF$ = 16.80 cm, then find $BC$.
Option 1: 7.5 cm
Option 2: 9.8 cm
Option 3: 8.7 cm
Option 4: 11.4 cm
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Correct Answer: 9.8 cm
Solution :
Given, $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are similar triangles.
$\therefore$ The ratio of their area will be equal to the ratio of squares of their lengths.
⇒ $\frac{49}{144} = \frac{\text{BC }^2}{(16.80)^2}$
⇒ $\text{BC} = \sqrt{\frac{49}{144}\times(16.8)^2}$
⇒ $\text{BC} =16.8\times \frac{7}{12}$
⇒ $\text{BC} = 9.8\ \mathrm{cm}$
Hence, the correct answer is 9.8 cm.
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