SOLUTION: 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 l

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Question 1058929: 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
Answer by ikleyn(52781) About Me  (Show Source):
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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

x%5E2+%2B+y%5E2 = 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

x%5E2+%2B+y%5E2 = 1125,             (1)
2x + y = 75.                (2)

From (2), express y = 75 - 2x and substitute it into (1) instead of y. You will get

x%5E2+%2B+%2875-2x%29%5E2 = 1125.

Simplify:

5x%5E2+-+300y+%2B+5625 = 1125,

5x%5E2+-+300y+%2B+4500 = 0,

x%5E2+-+60x+%2B+900 = 0.

%28x-30%29%5E2 = 0.

x = 30 is the solution.

Answer.  x = 30 ft,  y = 75-2x = 75-2*30 = 15 ft.