Question

If $△ABC\sim △DEF$ such that AB = 5 cm, area $\left(△ABC\right)=20{cm}^2$ and area $\left(△DEF\right)=45{cm}^2$, determine DE.

Answer 1

Given $△ABC\sim △DEF$

Hence the ratio of their areas is the ratio of squares of their sides

$\therefore \frac{ar\left(△ABC\right)}{ar\left(△DEF\right)}=\frac{A{B}^2}{D{E}^2}$

$\Rightarrow \frac{20}{45}=\frac{25}{D{E}^2}$

$\therefore DE=7.5$ cm