Question

If $△ABC\sim △DEF$ and if $ar\left[△ABC\right]:ar\left[△DEF\right]=16:25$, $BC=2.2cm$ then find $EF$.

Answer 1

For similar triangles,

ratio of area of triangles $=$ ratio of square of corresponding sides

Hence, $\frac{Ar.△ABC}{Ar.△DEF}=\frac{A{B}^2}{D{E}^2}$

$\frac{16}{25}=\frac{B{C}^2}{E{F}^2}$

$E{F}^2=\frac{25}{16}(2.2\times 2.2)$

$E{F}^2=7.5625$

$EF=2.75cm$