Question

$ABCD$ is a trapezium such that $BC\parallel AD$ and $AD=4cm$. If the diagonal AC and BD intersects at E.such that $\frac{AE}{EC}=\frac{DE}{BE}=\frac{1}{2}$. Then find BC.

Answer 1

$\frac{AE}{EC}=\frac{DE}{BE}=\frac{1}{2}$

In $\Delta ABD$ and $\Delta BEC$

$\angle BEC=\angle AED$

$\frac{AE}{EC}=\frac{DE}{EB}$

$\therefore \Delta BEC\sim \Delta AED$

$\therefore \frac{AE}{EC}=\frac{EB}{BE}=\frac{AD}{BC}=\frac{1}{2}$

$2AD=BC$

$BC=2\times 4=8$