Question

∆ABC ∼ ∆DEF such that ar(∆ABC) = 36 cm² and ar(∆DEF) = 49 cm².
Then, the ratio of their corresponding sides is
(a) 36 : 49
(b) 6 : 7
(c) 7 : 6
(d) $\sqrt{6}:\sqrt{7}$

Answer 1

(b) 6:7

$\because$ ∆ABC ∼ ∆DEF

$$\begin{gathered} \therefore \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}...\left(\mathrm{i}\right) \\ \mathrm{Also}, \\ \frac{ar(△ABC)}{ar(△DEF)}=\frac{A{B}^2}{D{E}^2} \\ \Rightarrow \frac{36}{49}=\frac{A{B}^2}{D{E}^2} \\ \Rightarrow \frac{6}{7}=\frac{AB}{DE} \\ \Rightarrow \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{6}{7}(\mathrm{from}(\mathrm{i}\left)\right) \\ \mathrm{Thus},\mathrm{the}\mathrm{ratio}\mathrm{of}\mathrm{corresponding}\mathrm{sides}\mathrm{is}6:7. \end{gathered}$$