## Dividing Right-Angled Figure

Dividing Right-Angled Figure
Divide the rectilinear right-angled figure shown below into two equal areas with one straight line $\overleftrightarrow{PP'}$.

Source: Julia Robinson Mathematics Festival

SOLUTION

Area of right-angled figure = area of $1\times 2$ rectangle + area of $1\times 1$ square
$=1\times 2+1\times 1$
$=3$

We want the area of triangle $APP'$ to be half of the area of the right-angled figure
$\frac{1}{2}AP'\left (AP\right )=\frac{3}{2}$
$AP'\left (AP\right )=3$
$AP'\left (2\right )=3$
$AP'=1.5$

The straight line $\overleftrightarrow{PP'}$ divides the right-angled figure into two equal areas.