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?
.
"area bordered by the outside edge of the path" minus "area of garden" equals "area of the path"
.
Let x = width of path
.
"area bordered by the outside edge of the path" = (18+2x)(13+2x)
"area of garden" = 18*13
"area of the path" = 516
.
(18+2x)(13+2x) - (18*13) = 516
234 + 26x + 36x + 4x^2 - 234 = 516
62x + 4x^2 = 516
4x^2 + 62x - 516 = 0
x^2 + 13x - 129 = 0
.
Can't be factored easily so you must use the quadratic equation. Doing so, will produce a positive and a negative solution. Since a negative answer doesn't make sense, the positive solution will be your answer.
x = 6.586 feet
.
Below is the quadratic solution:
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=685 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 6.5862523283024, -19.5862523283024.
Here's your graph:
 |
