If ΔABC ~ ΔDEF and area (ΔABC) : area (ΔDEF) = 49 : 100. Then DE : AB = ……………  (A) 9 : 10 

Correct option is (B) 10 : 7

We know that the areas of similar triangle are in the ratio of squares of their corresponding sides.

\(\because\) Given that \(\frac{ar(\triangle ABC)}{ar(\triangle DEF)}=\frac{49}{100}\)

\(\Rightarrow\) \((\frac{AB}{DE})^2=\frac{49}{100}\)    \(\left(\because\frac{ar(\triangle ABC)}{ar(\triangle DEF)}=(\frac{AB}{DE})^2=(\frac{BC}{EF})^2=(\frac{AC}{DF})^2\right)\)

\(\Rightarrow\) \(\frac{AB}{DE}=\sqrt{\frac{49}{100}}\)

\(=\frac{\sqrt{49}}{\sqrt{100}}=\frac7{10}\)

\(\therefore\frac{DE}{AB}=\frac{10}7\)

Hence, \(DE:AB=10:7\)

Correct option is: (B) 10 : 7