Question

∆ ABC ∼ ∆ DEF and their areas are respectively 64 cm² and 121 cm². If EF = 15.4 cm, find BC.

Answer 1

It is given that $△ABC~△DEF$.
Therefore, ratio of the areas of these triangles will be equal to the ratio of squares of their corresponding sides.

$$\begin{gathered} \frac{ar(△ABC)}{ar(△DEF)}=\frac{B{C}^2}{E{F}^2} \\ \mathrm{Let}BC\hspace{0.17em}\mathrm{be}x\mathrm{cm}. \\ \Rightarrow \frac{64}{121}=\frac{x^2}{(15.4{)}^2} \\ \Rightarrow x^2=\frac{64\times 15.4\times 15.4}{121} \\ \Rightarrow x=\sqrt{\frac{64\times 15.4\times 15.4}{121}} \\ =\frac{8\times 15.4}{11} \\ =11.2 \end{gathered}$$

Hence, BC = 11.2 cm