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.

Answer: Given in solution.

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About mvtrinh

Retired high school math teacher.
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