Question 953300: A 15m by 21m rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 567m2
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A 15m by 21m rectangular garden is to have a gravel path of uniform width bordering it.
How wide is the path if the total area covered by the garden and path is 567m2
:
Let x = the width of the gravel path
:
The garden is 15 by 21, therefore the overall dimensions, which include the path will be:
(2x + 15) by (2x + 21)
The overall area then
(2x+15)*(2x+ 21) = 567
FOIL
4x^2 + 42x + 30x + 315 = 567
4x^2 + 72x + 315 - 567 = 0
A quadratic equation
4x^2 + 72x - 252 = 0
Simplify, divide by 4
x^2 + 18x - 63 = 0
Factors to
(x + 21)(x - 3) = 0
the positive solution is all we want here
x = 3 meter is the width of the path
:
:
Check this, the overall dimensions add 6 m to each dimension of the garden
27 * 21 = 576
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