Question

A farmer wants to make a fenced area for his chickens. He has 120 feet of fencing available and his goal is to get the largest possible area so his chickens have the most room to live in which shape should he create with the fences, in order to achieve a maximum area for the given amount of fencing, he has.

Answer 1

To achieve the maximum area for the given amount of fencing (120 feet), the farmer should create a rectangular enclosure.

Step-by-step explanation:

Let's call the length of the rectangle "L" and the width "W." The perimeter of the rectangle, given the fencing available, is:

2L + 2W = 120 feet.

To maximize the area, he should solve for one variable in terms of the other and then find the maximum area:

2L + 2W = 120

2L = 120 - 2W

L = 60 - W

Now,to maximize the area (A), we use the formula for the area of a rectangle:

A = L * W

Substitute the expression for L:

A = (60 - W) * W

To find the maximum area, you can use calculus or trial and error to find the value of W that maximizes this function. In this case, it would be when W is 30 feet, and L is also 30 feet. This creates a square, which, as mentioned earlier, maximizes the area for a given perimeter.

So, the farmer should create a square enclosure with the 120 feet of fencing available to provide the largest possible area for his chickens.