Dividing Land

A man leaves a piece of land (see below) to his four sons, with instructions that it should be divided up into 4 equal pieces, each having the same shape as the original piece of land. How can this be achieved?

Source: Julia Robinson Mathematics Festival

SOLUTION
Area of land (trapezoid)
\frac{1}{2}100\left (100+200\right )=50\left (300\right )
=15000 \text{ yds}^2

Area of each subdivided piece
15000\div 4=3750 \text{ yds}^2

Each subdivided piece has the same shape as the original land requires that
3750=\frac{1}{2}x\left (x+2x\right ) where x is the length of the smaller base of the new trapezoid.
2\left (3750\right )=x^2+2x^2
7500=3x^2
x^2=2500
x=\pm 50
x=50 yds

The land is subdivided as shown below

Answer: Given in solution.

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About mvtrinh

Retired high school math teacher.
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