SOLUTION: Suppose that a strip of uniform width is plowed along both sides and both ends of a garden that is 120 ft long by 90 ft wide. How wide is the strip, if the garden is one-half plowe

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Question 560875: Suppose that a strip of uniform width is plowed along both sides and both ends of a garden that is 120 ft long by 90 ft wide. How wide is the strip, if the garden is one-half plowed?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that a strip of uniform width is plowed along both sides and both ends of a garden that is 120 ft long by 90 ft wide.
How wide is the strip, if the garden is one-half plowed?
:
Find the total area of the garden: 120 * 90 = 10800 sq/ft
Find half the area of the garden: 10800/2 = 5400 sq/ft
:
Let x = the width of the plowed strip all the way around.
:
The dimension of the unplowed area will be (120-2x) by (90-2x)
:
We know the area of the unplowed = the area of the plowed (5400 sq/ft)
:
Plowed area = unplowed area
(120-2x)*(90-2x) = 5400
FOIL
10800 - 240x - 180x + 4x^2 = 5400
Combine like terms
4x^2 - 420x + 10800 - 5400 = 0
4x^2 - 420x + 5400 = 0
Simplify divide by 4
x^2 - 105x + 1350 = 0
You can use the quadratic formula to solve this, but it will factor to:
(x-90)(x-15) = 0
only one solution will make sense here
x = 15 ft is the width of the plowed strip
;
:
See if this checks out
(120-2(15)) * (90-2(15) =
90 * 60 = 5400 sq/ft which is half the total area