Question

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

Answer 1

Since $△ABC\sim △DEF$

We know that if two triangles are similar,

Ratio of areas is equal to a square of the ratio of its corresponding sides

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

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

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

$\Rightarrow BC=\frac{8}{11}\times 15.4=8\times 1.4=11.2$

Hence $BC=11.2cm$