Let $∆ABC \sim ∆DEF$ and their areas be respectively $64\ cm^2$ and $121\ cm^2$. If $EF = 15.4\ cm$, find BC.

Given:

Let $∆ABC \sim ∆DEF$ and their areas be respectively $64\ cm^2$ and $121\ cm^2$.

$EF = 15.4\ cm$

To do:

We have to find BC.

Solution:

We know that,

The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.

Therefore,

$\frac{\operatorname{ar}(\triangle \mathrm{ABC})}{\operatorname{ar}(\Delta \mathrm{DEF})}=\frac{\mathrm{BC}^{2}}{\mathrm{EF}^{2}}$

This implies,

$\frac{64}{121}=\frac{\mathrm{BC}^{2}}{(15.4)^{2}}$

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

$\mathrm{BC}=\frac{8 \times 15.4}{11}$

$BC=11.2\ cm$