Question

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

Answer 1

Since $△ABC\sim △DEF$

We know that if two triangles are similar, then ratio of areas is equal to square of ratio of its corresponding sides.

Hence,$\frac{ar\left(△ABC\right)}{ar\left(△DEF\right)}={\left(\frac{BC}{EF}\right)}^2$

Putting the values,

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

$\Rightarrow {BC}^2=\frac{64}{121}\times {15.4}^2$

$\therefore BC=\frac{8}{11}\times 15.4=11.2cm$

Hence $BC=11.2cm$