SOLUTION: A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path?

Question 65774: A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path?

Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
(30-2x)(20-2x)=400
600-40x-60x+4x^2=400
4x^2-100x=-600+400
4x^2-100x=-200
4x^2-100x+200=0
x^2-25x+50=0
using the quadratic equation for x we get
x=(-b+-sqrt[b^2-4ac])/2a
x=(25+-sqrt625-4*1*50])/2*1
x=(25+-sqrt[625-200])/2
x=(25+-sqrt425)/2
x=(25+-20.6155)/2
x=(25+20.6155)/2
x=45.6155/2
x=22.8 not a solution because it is longer than the garden.
x=(25-20.6155)/2
x=4.3845/2
x=2.19 feet for the path

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