SOLUTION: help me someone please? i am so lost with this. Construction. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden

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Question 79245: help me someone please? i am so lost with this.
Construction. A garden area is 30 ft long and 20 ft 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 stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A garden area is 30 ft long and 20 ft 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?
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Draw the picture of the garden; Draw the path inside the perimeter of the garden.
Let the width of the path be "x".
Note: The area of the garden is now less than what it was before the
path was built.
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EQUATIONS:
New area of the garden is (30-2x)(20-2x)=4[(15-x)(10-x)]sq. ft.
This remaining garden area is 400 sq ft.
4(15-x)(10-x)=400
(15-x)(10-x)=100
x^2-25x+150=100
x^2-25x+50=0
x=[25+-sqrt(625-4*50]/2
x=[25+-sqrt425]/2
x=[25+-5sqrt17]/2
x=(25+5sqrt17)/2 = 22.81 ft or x=(25-5sqrt17)/2= 2.19 ft
Only reasonable answer = 2.19 ft.
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Cheers,
Stan H.