miguel buys 100 feet of fence to enclose a rectangular area of his backyard so his dog run freely. What is the maximum area, in square feet, he can enclose

The maximum area he can enclose is 625 sq. ft.

In order to maximize area and minimize perimeter, we use dimensions that are as close to equal as possible. We have 100 ft of fence for a 4-sided figure; 100/4 = 25 ft per side.

With a length of 25 and a width of 25, we would have an area of 25(25) = 625 sq ft.

Answer Link

facundo3141592 facundo3141592 · Answer 2 · 2022-04-15T13:59:39+02:00

By using what we know about quadratic equations, we will see that the maximum area is 625 ft^2

How to get the maximum area?

We know that for a rectangle of length L and width W, the area is:

A = L*W

And the perimeter is:

P = 2*(W + L).

In this case, we know that the perimeter is 100ft, then we write:

100ft = 2*(W + L).

Now we can isolate one of the variables in the above equation:

100ft/2 = W + L

50ft - L = W

Now we can replace W on the area equation:

A = L*W = L*(50ft - L)

A = L*50ft - L^2

Notice that this is a quadratic equation of negative leading coefficient, thus, the maximum is at the vertex.

Remember that for a quadratic equation:

y = a*x^2 + b*x + c

The x-value of the vertex is:

x = -b/2a

So, in our case:

A = L*50ft - L^2

The vertex is at:

L = -50ft/(2*-1) = 25ft

L = 25ft

Then the maximum area is:

A = 25ft*50ft - (25ft)^2 = 625 ft^2

If you want to learn more about quadratic equations, you can read:

https://brainly.com/question/1214333