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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,
$\frac{64}{121}=\frac{\mathrm{BC}^{2}}{(15.4)^{2}}$
$\frac{8}{11}=\frac{\mathrm{BC}}{15.4}$
$\mathrm{BC}=\frac{8 \times 15.4}{11}$
$BC=11.2\ cm$
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