Question

In the following figure, $segBE\perp segAB$ and $segAB\perp segAD$. If $BE=6$ and $AD=9$, find $\frac{A\left(△ABE\right)}{A\left(△BAD\right)}$

Answer 1

$A\left(△ABE\right)=\frac{1}{2}\times BE\times AB=\frac{1}{2}\times 6\times AB$

$A\left(△BAD\right)=\frac{1}{2}\times AD\times AB=\frac{1}{2}\times 9\times AB$

$\frac{A\left(△ABE\right)}{A\left(△BAD\right)}=\frac{\frac{1}{2}\times 6\times AB}{\frac{1}{2}\times 9\times AB}=\frac{6}{9}=\frac{2}{3}$