Question 172635
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?