SOLUTION: A rectangular plot, 4 meters by 8 meters, is to be used for a garden. The owner decides to put a pavement of uniform width inside the entire border so that 12 square meters of the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A rectangular plot, 4 meters by 8 meters, is to be used for a garden. The owner decides to put a pavement of uniform width inside the entire border so that 12 square meters of the       Log On


   

Question 1199222: A rectangular plot, 4 meters by 8 meters, is to be used for a garden. The owner decides to put a pavement of uniform width inside the entire border so that 12 square meters of the plot is left for flowers. How wide should the pavement be?
Found 3 solutions by Shin123, josgarithmetic, ikleyn:
Answer by Shin123(626) About Me  (Show Source):
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Let the pavement width be x. Then, the dimensions of the rectangle that is left is 4-2x by 8-2x. We know that this equals 12, so we have %284-2x%29%2A%288-2x%29=12. Expanding, we get 4x%5E2-24x%2B32=12. Subtracting 12 from both sides, we get 4x%5E2-24x%2B20=0. To simplify the quadratic, we can divide both sides by 4 to get x%5E2-6x%2B5=0. We can easily factor this to get %28x-1%29%28x-5%29=0. Note that x=5 won't work in our case because the dimensions of the rectangle can't be negative. Therefore, the pavement should be 1 meter long.

Answer by josgarithmetic(39621) About Me  (Show Source):
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Total area, 4%2A8 square meters
Area of remaining plot for the flowers, %284-2w%29%288-2w%29 for w uniform width border

%284-2w%29%288-2w%29=12
Solve for w.

Simplify first...
2%2A2%2A%282-w%29%284-w%29=2%2A2%2A3
%282-w%29%284-w%29=3
Could these factors of 3 be 1 and 3 ?
Trying this,
2-w=1
2-1=w
w=1
-
OR
4-w=3
4-3=w
w=1
-
The uniform width of the inside border is 1 cross%28foot%29meter.

Answer by ikleyn(52817) About Me  (Show Source):
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.

Correction to the answer by @josgarithmetic:

        The uniform width of the inside pavement is 1 meter   (definitely,  not 1 foot).



Correction to the answer by @shin123:

        The pavement should be 1 meter wide   (definitely,  not 1 meter long).