We know that the area is determined by the equation
And the width is
First of all, remember that the area of a rectangle is
Where the length would be
Before we use this length expression, first we need to find the solutions for the given quadratic equation. Using a calculator, the solutions are 2/3 and -2. Only the number 2/3 makes sense to the problem since length can't be negative.
Expressing these solutions as factors would be
Now, we replace all factors to find the length
Therefore, the length is (3x-2) feet.
On the other hand, the perimeter is the sum of all sides, also it can be expressed as
Using the length and width expressions
Therefore, the perimeter is (8x) feet.
When <em>x</em> is 6, the area would be
The area is 128 square feet. Now, if the cost of the fertilizer is $0.25, the total cost for the area would be