Question

Mr. Johnson wants to build a pen as large as possible for his dogs but unfortunatiey he only has 24 feet of fencing he does get not want his dogs to get out so there should be no gaps or holes

1) what’s the largest possible pen he can make for his pigs using the fence he has

Answer 1

To maximize the area of the pen, Mr. Johnson should build a rectangular pen with dimensions 6 feet by 6 feet.

Step-by-step explanation:

The largest possible pen Mr. Johnson can make for his dogs using the 24 feet of fencing

To determine the largest possible pen, we need to find the dimensions that maximize the area of the pen. A rectangular pen would likely be the most efficient use of the fencing. Let's denote the width of the pen as 'w' and the length as 'l'.

The perimeter of the pen is given by the formula: P = 2w + 2l. Since Mr. Johnson has 24 feet of fencing, we can set up the equation 2w + 2l = 24.

Next, we can solve for one variable in terms of the other. For example, if we solve for w, we get w = 12 - l.

To maximize the area of the pen, we can use the formula: A = wl. Substituting the expression for w from the previous step, we have A = (12 - l)l = 12l - l^2.

To find the maximum area, we can take the derivative of A with respect to l, set it equal to zero, and solve for l. The maximum area occurs when l = 6 feet. Substituting this value back into the expression for w, we get w = 6 feet.

Therefore, the largest possible pen Mr. Johnson can make for his dogs using the 24 feet of fencing is a rectangular pen with dimensions 6 feet by 6 feet.