Question

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

Answer 1

Construction:
Draw AO perpendicular to BC and DP perpendicular to EF
Also,
$△ABC$ $\sim$ $△DEF$

$\therefore$ $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{AO}{DP}$

$\therefore$ $\frac{A\left(△ABC\right)}{A\left(△DEF\right)}$ $=\frac{\frac{1}{2}\times BC\times AO}{\frac{1}{2}\times EF\times DP}$

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

$\therefore$ $\frac{64}{121}=\frac{B{C}^2}{{15.4}^2}$

$\therefore$ $BC=11.2cm$