Question 56309: Thank you all for your help. I have a construction question.
if a garden area is 30 ft long and 20ft wide. A path of uniform width is set around the edge. if the remaining garden area is 400 ft. what is the width of the path?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! If a garden area is 30 ft long, and 20 ft wide and a path of uniform width is set around the edge and if the remaining garden area is 400 ft. what is the width of the path?
I understand that a 30 by 20 ft area will contain a rectangular garden of 400 sq ft and a path around it.
:
Draw a diagram labelling a rectangle 30 by 20, inside this area is a path all the way around the garden with a width of x
:
The garden dimensions would be: (30-2x) by (20-2x), this area is 400 sq ft
(30-2x) * (20-2x) = 400
FOIL:
600 - 60x - 40x + 4x^2 = 400
4x^2 - 100x + 600 - 400 = 0
:
A quadratic equation:
4x^2 - 100x + 200 = 0
:
Simplify, divide equation by 4 and you have:
x^2 - 25x + 50 = 0
:
Unfortunately, this will not easily factor, using the quadratic formula with:
a = 1; b = -25, c = +50; the solutions were:
x = +22.81 and x = 2.19,
:
Obviously the path width would have to be 2.19 ft wide
:
:
We can check that to see if the garden dimensions have an area of 400
:
[30 - 2(2.19)] * [20 - 2(2.19)] =
(30 - 4.38) * (20 - 4.38) =
25.62 * 15.62 = 400.1844 ~ 400 sq ft
:
Did this make sense to you on this fine Sunday Morning?
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