Question

Carol has 1100 feet of fencing to fence in a rectangular horse corral
Find a function that models the area A of the corral in terms of the width x of the corral A(x)
Find the dimensions of the rectangle that maximize the area of the corral
Width and length in ft

Answer 1

To find a function that models the area A of the corral in terms of the width x, we can assume that the length of the corral is also x. Therefore, the area of the corral can be represented as:

A(x) = x * x = x^2

To find the dimensions of the rectangle that maximize the area of the corral, we can use the fact that Carol has 1100 feet of fencing. The perimeter of the rectangle will be equal to the total length of fencing, so we have:

2x + 2x = 1100
4x = 1100
x = 275

Therefore, the width of the corral is 275 ft and the length is also 275 ft.