SOLUTION: Can someone please help me I came up with three crazy answer. thank you A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be bui

Question 172635This question is from textbook
: Can someone please help me I came up with three crazy answer. thank you

A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet?
This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of
uniform width is to be built around the garden.
How wide can the path be, if there is enough gravel for 516 square feet?
:
Let x = the width of the path required to utilize 516 sq/ft of gravel
then
The overall dimensions (including the path) are: (2x+18) by (2x+13)
FOIL this and we have:
4x^2 + 62x + 234 = the area of the garden and the path
:
18 * 13 = 234, the area of the garden
:
Overall area - garden area = path area (516 sq/ft)
:
(4x^2 + 62x + 234) - 234 = 516
;
4x^2 + 62x - 516 = 0
Simplify divide by 2:
2x^2 + 31x - 258 = 0
This will factor:
(2x + 43)(x - 6) = 0
Positive solution
x = + 6 ft is the width of the path
:
:
Check our solution:
overall dimensions would be 30 by 25 = 750 sq/ft (add 12 to length & width)
750 - 234 = 516, the area of the path
:
Did this clear up some of the difficulty you were having here?
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