SOLUTION: A garden area is 30 ft 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 60937: A garden area is 30 ft 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=0
4x^2-100x+200=0
x^2-25x+50=0
using the quadratic equation x=(-b+-sqrt[b^2-4ac])/2a we get
x=(-25+-sqrt[625-4*1*50])/2*1
x=(-25+-sqrt[625-200])/2
x=(-25+-sqrt425)/2
x=(-25+-20.6)/2
x=(-25+20.6)/2
x=-4.4/2
x=-2.2 solution
x=(-25-20.6)/2
x=-45.6/2
x=-22.8 solution
seeing as one of these sidesare only 20 ft we can ignore this solution
proof using the first soluition we get
(30-2*2.2)+(20-2*2.2)=400
(30-4.4)(20-4.4)=400
25.6*15.6=400
400=400

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