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, \(DE:AB=10:7\)
