Question

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

Answer 1

Find the length of given line segment:

As,$\Delta ABC~\Delta DEF$

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

So,

$\Rightarrow$ $\frac{\mathbf{Area}\left(△\mathrm{ABC}\right)}{\mathbf{Area}\left(△\mathrm{DEF}\right)}\mathbf{=}{\mathbf{\left(}\frac{\mathbf{BC}}{\mathbf{EF}}\mathbf{\right)}}^{\mathbf{2}}$

$\Rightarrow$ $\frac{64}{121}=\frac{B{C}^2}{15.4^2}$

$\Rightarrow$ $\frac{8}{11}=\frac{BC}{15.4}$

$\Rightarrow$ $BC=11.2cm$

Hence, the length of $\mathit{B}\mathit{C}$ is $\mathbf{11}\mathbf{.}\mathbf{2}\mathbf{}\mathit{c}\mathit{m}$