waecmaths question:
In a parallelogram, PQRS, $\overline{QR}$ is produced to M such that $\left| QR \right|=\left| RM \right|$. What fraction of the area of PQMS is the area of PRMS
Option A:
$\tfrac{1}{4}$
Option B:
$\tfrac{1}{3}$
Option C:
$\tfrac{2}{3}$
Option D:
$\tfrac{3}{4}$
waecmaths solution:
\[\begin{align} & Area\text{ }of\text{ }PQRS=bh \\ & Area\text{ }of\text{ }PQMS=\tfrac{1}{2}(b+2b)h=\tfrac{3}{2}bh \\ & \text{The fraction of the area }PQMS\text{ of }PRMS=\frac{bh}{\tfrac{3}{2}bh}=\frac{2}{3} \\\end{align}\]