SOLUTION: a garden area is 30ft long and 20ft wide. a path of uniform width is set around the edge. if the remaining garden is 400ft squared.what is the width of the path?

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Question 59540: a garden area is 30ft long and 20ft wide. a path of uniform width is set around the edge. if the remaining garden is 400ft squared.what is the width of the path?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Draw the picture with one rectangle inside another.
The inner rectangle area is 400 sq ft.
The outer rectangle has area 600 sq ft including the path area.
Let the path have uniform width of "x" ft.
Notice the four rectangles nor surrounding the inner
rectangle.
Two of them are 20 ft by x ft: Area of each is 20x ft: Total for the two is 40x
Two of them are (30-2x) by x ft: Area of each of these is 30x-2x^2; Total for
the two is 60x-4x^2'
EQUATION:
Outer rectangle area - inner rectangle area =200 sq ft.
The path covers that 200 sq ft.
Path area = 40x+60x-4x^2 = 200 sq ft.
4x^2-100x+200=0
x^2-25x+50=0
x=[25+-sqrt(25^2-4*50]/2
x=[25+-sqrt(425)]/2
x=[25+-5sqrt17]/2
x=4.38/2=2.1922 ft. (width of the sidewalk)
Cheers,
Stan H.