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?

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


Hope this helps----ptaylor