SOLUTION: Construction. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path?

Question 78361: Construction. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path?
:
draw this as a 30 by 20 rectangle with a uniform path. Label the width of this
path as x. It becomes apparent that the dimensions inside the path, which is given
as 400 sq ft, is (30-2x) by 20-2x).
:
(30-2x) * (20-2x) = 400
600 - 100x + 4x^2 = 400
600 - 400 - 100x + 4x^2 = 0; subtracted 400 from both sides
:
Arrange as a quadratic equation:
4x^2 - 100x + 200 = 0
:
Simplify, divide equation by 4:
x^2 - 25x + 50 = 0
:
Use the quadratic formula so find x: a=1; b=-25; c=50
:
only one of the solutions will make sense. I got ~ 2.2 ft
:
Check it:
(30-4.4) * (20-4.4) =
25.6 * 15.6 = 399.36 ~ 400, confirms our solution
:
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