Question

Let $\Delta ABC~\Delta DEF$ and their areas be, respectively, $64c{m}^2$ and $121c{m}^2$. If $EF=15.4cm$, find $BC$?

Answer 1

Find the length of BC of similiar triangle:

We know that, $\Delta ABC~\Delta DEF$

Ratio of areas of two similar triangles is proportional to the square of the ratio of their corresponding sides.

Therefore,

$\mathbf{}\mathbf{}\frac{\mathbf{Area}\mathbf{}\mathbf{of}\mathbf{}\mathbf{∆}\mathbf{ABC}}{\mathbf{Area}\mathbf{}\mathbf{of}\mathbf{}\mathbf{∆}\mathbf{DEF}}\mathbf{=}\frac{{\mathbf{BC}}^{\mathbf{2}}}{{\mathbf{EF}}^{\mathbf{2}}}$

$$\begin{gathered} \frac{\mathrm{Area}\mathrm{of}∆\mathrm{ABC}}{\mathrm{Area}\mathrm{of}∆\mathrm{DEF}}=\frac{64}{121} \\ \Rightarrow \frac{B{C}^2}{E{F}^2}=\frac{64}{121} \\ \Rightarrow {\left(\frac{BC}{EF}\right)}^2={\left(\frac{8}{11}\right)}^2 \\ \Rightarrow \frac{BC}{EF}=\frac{8}{11} \\ \Rightarrow \frac{BC}{15.4}=\frac{8}{11} \\ \Rightarrow BC=\frac{8}{11}\times \left(15.4\right) \\ \Rightarrow BC=11.2cm \end{gathered}$$

Hence, $\mathit{B}\mathit{C}$ is equal to $\mathbf{11}\mathbf{.}\mathbf{2}\mathbf{}\mathit{c}\mathit{m}$