SOLUTION: A rectangular garden has dimensions of 18 ft by 13 ft. 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 s

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A rectangular garden has dimensions of 18 ft by 13 ft. 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 s      Log On


   

Question 149896This question is from textbook
: A rectangular garden has dimensions of 18 ft by 13 ft. 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 checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
18*13=234 ft^2 for the garden.
234+516=750 is the area for the garden plus the path.
(18+2x)(13+2x)=750
234+36x+26x+4x^2=750
4x^2+62x+234-750=0
4x^2+62x-516=0
2(2x^2+31x-258)=0
2(2x+43)(x-6)=0
x-6=0
x=6 for the width of the path.
proof:
(18+2*6)(13+2*6)+750
(18+12)(13+12)=750
30*25=750
750=750