Final answer:
To maximize the area of the rectangular garden, we can use the formula for area and the given information about the total length of the fencing. By solving for the dimensions that maximize the area, we can find the length and width of the garden.
Step-by-step explanation:
In order to find the dimensions of the garden that will maximize its area, we can use the formula for the area of a rectangle: Area = length x width. Let's assume that the length of the garden is L and the width is W.
We are given that the total length of the fencing is 80 m. Since the fencing goes around the perimeter of the garden, we have: 2L + W = 80.
Now, to maximize the area of the garden, we can use the equation for area in terms of one variable. We can solve the equation from step 2 for L: L = (80 - W)/2.
Substitute the expression for L in the area formula to obtain: Area = ((80 - W)/2) x W.
To find the maximum area, we can differentiate the area equation with respect to W and set the derivative equal to zero: d(Area)/dW = 0.
Solve the equation from step 5 for W to obtain the value of W that maximizes the area.
Substitute the value of W from step 6 into the equation for L from step 3 to find the corresponding value of L.