SOLUTION: a gardener has 61 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. If the length of the garden is to be twice its width, wha

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: a gardener has 61 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. If the length of the garden is to be twice its width, wha      Log On

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Question 263582: a gardener has 61 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. If the length of the garden is to be twice its width, what will be the dimensions of the garden?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = width of garden in ft
Let b = length of garden in ft
given:
b+=+2a
The equation for perimeter is
p+=+2%2A%28a+%2B+4%29+%2B+2%2A%28b+%2B+4%29 (note that I add 4 ft to the width and length
to account for the path around the garden)
61+=+2%2A%28a+%2B+4%29+%2B+2%2A%28b+%2B+4%29
61+=+2a+%2B+8+%2B+2b+%2B+8
61+=+2a+%2B+2b+%2B+16
2a+%2B+2b+=+45
And, since b+=+2a
2a+%2B+2%2A2a+=+45
6a+=+45
a+=+7.5
b+=+2a
b+=+15
The width is 7.5 ft and the length is 15 ft
check:
61+=+2%2A%28a+%2B+4%29+%2B+2%2A%28b+%2B+4%29
61+=+2%2A%287.5+%2B+4%29+%2B+2%2A%2815+%2B+4%29
61+=+2%2A11.5+%2B+2%2A19
61+=+23+%2B+38
61+=+61
OK