Triangle ABC and DEF are similar. If area ( ) = 36cm^2, area ( ) … - Vidyadip

Question

Triangle $ABC$ and $DEF$ are similar.
If area $\big(\triangle\text{ABC}\big) = 36\text{cm}^2,$ area $\big(\triangle\text{DEF}\big) = 64\text{cm}^2$ and $DE = 6.2\ cm,$ find $AB.$

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Answer

$\because\triangle\text{ABC}\sim\triangle\text{DEF},$
$\therefore\frac{\text{area}(\triangle\text{ABC)}}{\text{area}(\triangle\text{DEF)}}=\frac{\text{AB}^2}{\text{DE}^2}$
$\Rightarrow\frac{36}{64}=\frac{\text{AB}^2}{(6.2)^2}\Rightarrow\frac{(6)^2}{(8)^2}=\frac{\text{AB}^2}{(6.2)^2}$
$\Rightarrow\frac{\text{AB}}{6.2}=\frac{6}{8}\Rightarrow\text{AB}=\frac{6\times6.2}{8}=\frac{37.2}{8}$
$\Rightarrow\text{AB}=4.65$
Hence $AB = 4.65.$

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