a dog owner has 200ft of fencing and wants to enclose the greatest possible rectangular area for her dog .what dimension should she use

To find the dimensions that would enclose the greatest possible rectangular area within 200 feet of fencing, you can follow these steps:

Step 1: Understand the problem:
- The owner has 200ft of fencing.
- The goal is to find the dimensions that result in the greatest rectangular area.

Step 2: Define the variables:
- Let's assume the width of the rectangular area to be "w" (in feet).
- Let's assume the length of the rectangular area to be "l" (in feet).

Step 3: Set up the equation:
- Perimeter (P) of a rectangle is given by the formula:
P = 2 * (w + l)
- In this case, the perimeter is given as 200ft:
200 = 2 * (w + l)

Step 4: Solve for one variable:
- We can solve the equation in Step 3 for one variable. In this case, let's solve for "l":
100 = w + l
l = 100 - w

Step 5: Determine the area:
- The area (A) of a rectangle is given by the formula:
A = w * l
- Substitute the value of "l" from Step 4 into the area formula:
A = w * (100 - w)
A = 100w - w^2

Step 6: Find the maximum area:
- To find the maximum area, differentiate the area equation from Step 5 with respect to "w" and set it equal to 0:
dA/dw = 100 - 2w = 0
2w = 100
w = 50

Step 7: Substitute the value of "w" into the equation for "l" (from Step 4):
l = 100 - w
l = 100 - 50
l = 50

Step 8: Interpret the result:
- The dimensions that yield the greatest rectangular area within the given fencing are a width of 50ft and a length of 50ft.

Therefore, the dog owner should use dimensions of 50ft by 50ft to enclose the greatest possible rectangular area.

I bet it is a square.