Question 821677: a rectangular plot, 4 meters by 8 meter, is to be used for a garden. the owner decides to put a pavement of uniform width inside the entire borders so that 12 square meters of the plot is left for flowers. How wide should the pavement be?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a rectangular plot, 4 meters by 8 meter, is to be used for a garden.
the owner decides to put a pavement of uniform width inside the entire borders so that 12 square meters of the plot is left for flowers.
How wide should the pavement be?
:
Let x = the width of the pavement
Then the dimensions of the garden will be
(4-2x) by (8-2x)
:
The equation
(4-2x)*(8-2x) = 12
FOIL
32 - 8x - 16x + 4x^2 = 12
Arrange as a quadratic equation
4x^2 - 24x + 32 - 12 = 0
4x^2 - 24x + 20 = 0
Simplify, divide by 4
x^2 - 6x + 5 = 0
factors to
(x-5)(x-1) = 0
The reasonable solution
x = 1 meter is the width of pavement
:
:
See if that works
(4-2)*(8-2) = 12
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