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A farmer has 150 feet of fence available to enclose a 1125 square foot region in the shape of adjoining squares,
with sides of length x and y. The big square has sides of length x and the small square has sides of length y. Find x and y
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First equation is
= 1125. (1) for the area.
The second equation is
4x + 4y - 2y = 150. (2) for the perimeter (2y is distracted to account for the adjacent part of the two squares)
Simplifying (2), we have these two equations in the form
= 1125, (1)
2x + y = 75. (2)
From (2), express y = 75 - 2x and substitute it into (1) instead of y. You will get
= 1125.
Simplify:
= 1125,
= 0,
= 0.
= 0.
x = 30 is the solution.
Answer. x = 30 ft, y = 75-2x = 75-2*30 = 15 ft.