Question

In ∆ABC and ∆DEF, we have: $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{5}{7},$ then
ar(∆ABC) : ar(∆DEF) = ?

(a) 5 : 7
(b) 25 : 49
(c) 49 : 25
(d) 125 : 343

Answer 1

(b) 25 : 49

• $$\begin{gathered} \mathrm{In}△\mathrm{ABC}\mathrm{and}△\mathrm{DEF},\mathrm{we}\mathrm{have}: \\ \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{5}{7} \\ \mathrm{Therefore},\mathrm{by}\mathrm{SSS}\mathrm{criterion},\mathrm{we}\mathrm{conclude}\mathrm{that}△ABC~△DEF. \\ \Rightarrow \frac{ar(△ABC)}{ar(△DEF)}=\frac{A{B}^2}{D{E}^2}={\left(\frac{5}{7}\right)}^2=\frac{25}{49}=25:49 \end{gathered}$$