Question

∆ABC ∼ ∆DEF such that ar(∆ABC) = 64 cm² and ar(∆DEF) = 169 cm². If BC = 4 cm, find EF.

Answer 1

$\because$ ∆ABC ∼ ∆DEF

$$\begin{gathered} \therefore \frac{ar(△ABC)}{ar(△DEF)}=\frac{B{C}^2}{E{F}^2} \\ \Rightarrow \frac{64}{169}=\frac{4^2}{E{F}^2} \\ \Rightarrow E{F}^2=\frac{16\times 169}{64} \\ \Rightarrow EF=\frac{4\times 13}{8}=6.5\mathrm{cm} \end{gathered}$$