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The triangles $A B C$ and $D E F$ are similar. If their areas are $100 c m^{2}$ and $49 c m^{2}$ respectively and $B C = 8.2 c m$ , then $E F =$

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5.47 cm

5.74 cm

6.47 cm

6.74 cm

answer is B.

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Detailed Solution

\frac{[A B C]}{[D E F]} = \frac{B C^{2}}{E F^{2}}

$\frac{100}{49} = \frac{B C^{2}}{E F^{2}}$

$\frac{B C}{E F} = \frac{10}{7} \Rightarrow \frac{8.2}{E F} = \frac{10}{7}$

$E F = \frac{8.2 \times 7}{10} = 5.74 c m$ .

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