Question 1058929
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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^2 + y^2}}} = 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^2 + y^2}}} = 1125,             (1)
2x + y = 75.                (2)

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

{{{x^2 + (75-2x)^2}}} = 1125.

Simplify:

{{{5x^2 - 300y + 5625}}} = 1125,

{{{5x^2 - 300y + 4500}}} = 0,

{{{x^2 - 60x + 900}}} = 0.

{{{(x-30)^2}}} = 0.

x = 30 is the solution.

<U>Answer</U>.  x = 30 ft,  y = 75-2x = 75-2*30 = 15 ft.
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