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?
Gosh I am so lo
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Gosh I am so lo
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Question 65711: 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?
Gosh I am so lost on this one, thank you Found 2 solutions by ptaylor, josmiceli:Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! 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?
Let x= width of path
garden area=(l)(w)=(30)(20)=600 sq ft
remaining garden area=400 sq ft
Length of the remaining garden area =(30-2x) ft
Width of remaining garden area = (20-2x) ft, so
Eq(1) (30-2x)(20-2x)=400 expanding the factors, we have:
600-100x+4x^2=400 divide by 4
150-25x+x^2=100 subtract 100 from each side
x^2-25x+50=0 factors are:
Using the quadratic formula(x=(-b+or-sqrt(b^2-4ac))/2a we get
x=(25+or-sqrt(625-200))/2
x=(25+or-sqrt(425))/2
x=(25-20.6)/2
x=2.2 ft
x=(25+20.6)/2
x=22.8 ft Not a solution. It yields negative lengths and widths
Substitute x=2.2ft in (1) and we get
(30-4.4)(20-4.4)=400
(25.6)(15.6)=400
399+=400
You can put this solution on YOUR website! The garden area is
When the path around it is made, is left
for the garden
If the width of the path is x, the area,
is
solve with quadratic formula ft, answer
check
Unless I goofed, that's it
