Question

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

Answer 1

We have △ABC ∼ △DEF
If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.
$$\begin{gathered} \therefore \frac{\mathrm{area}\left(△\mathrm{ABC}\right)}{\mathrm{area}\left(△\mathrm{DEF}\right)}={\left(\frac{\mathrm{BC}}{\mathrm{EF}}\right)}^2 \\ \Rightarrow \frac{64}{169}={\left(\frac{\mathrm{BC}}{\mathrm{EF}}\right)}^2 \\ \Rightarrow {\left(\frac{8}{13}\right)}^2={\left(\frac{4}{\mathrm{EF}}\right)}^2 \end{gathered}$$
$$\begin{gathered} \Rightarrow \frac{8}{13}=\frac{4}{\mathrm{EF}} \\ \Rightarrow \mathrm{EF}=6.5\mathrm{cm} \end{gathered}$$