Answer:
Therefore, the dimensions the farmer should use are 60 feet by 90 feet or 90 feet by 60 feet to enclose an area of 3600 square feet with 300 feet of fencing.
Explanation:
To find the dimensions of the rectangular area that can be enclosed with 300 feet of fencing and an area of 3600 square feet, we can use the formula for the perimeter of a rectangle.
Let's assume the length of the rectangle is L and the width is W.
The formula for the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
In this case, the perimeter is given as 300 feet, so we can set up the equation:
300 = 2 * (L + W)
Simplifying the equation, we get:
150 = L + W
We also know that the area of the rectangle is 3600 square feet:
Area = Length * Width
3600 = L * W
Now we have a system of two equations:
150 = L + W
3600 = L * W
To solve this system of equations, we can use substitution.
Rearrange the first equation to solve for W:
W = 150 - L
Substitute this expression for W in the second equation:
3600 = L * (150 - L)
Expanding the equation, we get:
3600 = 150L - L^2
Rearrange the equation to get a quadratic equation in standard form:
L^2 - 150L + 3600 = 0
Now we can solve this quadratic equation to find the possible values of L. Once we have the values of L, we can substitute them back into the equation W = 150 - L to find the corresponding values of W.
Using factoring or the quadratic formula, we find that the possible values for L are 60 and 90.
For L = 60, W = 150 - 60 = 90.
For L = 90, W = 150 - 90 = 60.
Therefore, the dimensions the farmer should use are 60 feet by 90 feet or 90 feet by 60 feet to enclose an area of 3600 square feet with 300 feet of fencing.