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Answer :
Answer:
Given that,
Gerald purchases a rectangular plot of land.
The length of the plot is 20 feet more than the width.
Let l and w be the length and width of the rectangle respectively in feet.
we get, l=w+20
The cost of the land was $12 per square foot. Gerald also had a fence put around the entire perimeter of the plot, at a cost of $8 per linear foot.
The total amount he spent on both the land and the fence was $10,560
we get,
[tex]12\times(l\times w)+8(2\times(l+w))=10560[/tex]Substitute l, we get,
[tex]12w(w+20)+16(w+20+w)=10560[/tex][tex]12w^2+240w+32w+320=10560[/tex][tex]12w^2+272w-10240=0[/tex][tex]3w^2+68w-2560=0[/tex][tex]3w^2-60w+128w-2560=0[/tex][tex]3w(w-20)+128(w-20)=0[/tex]we get,
[tex](3w+128)(w-20)=0[/tex]The possible width of the rectangle is 20 feet.
Length of the width is 40 feet.
The required dimension of the rectangle is ,
Length is 40 feet and width is 20 feet.
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