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Chapter 11: Q. 87 (page 774)

Fencing: A farmer has 300 feet of fence available to enclose a 4500-square-foot region in the shape of adjoining squares, with sides of length x and y. See the figure. Findx and y.

Short Answer

Expert verified

x=60andy=30.

Step by step solution

01

Step 1. Form system of equations.

The dimensions of the fence are

Total perimeter =4x+2y.

Total length of fence given is 300 feet which gives

4x+2y=300

The area of the adjoining squares is 4500 square foot,

role="math" localid="1646894136795" x2+y2=4500

02

Step 2. Solve the system of equations.

From first equation,

4x+2y=3002x+y=150y=150-2x

From second equation,

x2+y2=4500x2+(150-2x)2=4500 5x2-600x+22500=45005x2-600x+18000=0x2-120x+3600=0

Using the quadratic equation formula, x=-b±b2-4ac2a

x=120±(-120)2-4(1)(3600)2(1)=120±14400-144002=120±02=1202=60

and

y=150-2(60)=150-120=30

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