SOLUTION: I am sooo stuck on this problem! I have attacked it from so many ways, and am getting more and more confused! PLEASE HELP! THANK YOU in advance! A garden area is 30ft long an

Question 59395: I am sooo stuck on this problem! I have attacked it from so many ways, and am getting more and more confused! PLEASE HELP! THANK YOU in advance!
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 400 square ft, what is the width of the path?
Step by step help would be so wonderful! Thanks again!
ac
Answer by stanbon(75887) (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 400 square ft, what is the width of the path?
----------
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.

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