Final answer:
To find the area of the largest rectangular field given a perimeter, you can use the steps outlined in the detailed answer.
Step-by-step explanation:
The area of the largest rectangular field when a perimeter is given can be found by using the following steps:
Let the length of the rectangle be l and the width be w.
Since the perimeter is given, we have: 2(l + w) = Perimeter.
Simplify the equation to get: l + w = Perimeter/2.
To find the maximum area, we need to maximize the value of lw. Using the equation from step 3, we can rewrite it as: l = Perimeter/2 - w.
Substitute the value of l from step 4 into the equation for area: Area = (Perimeter/2 - w)w.
To find the maximum area, we need to find the value of w that maximizes the expression from step 5.
Take the derivative of the expression from step 5 with respect to w and set it equal to 0 to find the critical points.
Determine the value of w that maximizes the area by evaluating the expression from step 5 at each critical point and including the endpoints of the interval.
Once you have the value of w, substitute it back into the expression from step 5 to find the maximum area.