16 * 20 = 320 square feet
Multiply the others to find the that gives the largest number of square feet.
16 feet by 20 feet
18 feet by 18 feet
14 feet by 22
12 feet by 24 feet
Multiply the others to find the that gives the largest number of square feet.
Let's assign the length as 'L' and the width as 'W'.
According to the problem, Mrs. Watterson has 72 feet of fencing available. The total perimeter of the rectangle will be equal to the sum of the lengths of all four sides, which is also equal to the total amount of fencing Mrs. Watterson has.
So, we can set up the equation:
2L + 2W = 72
Simplifying this equation, we get:
L + W = 36
Now we need to find the dimensions that will give us the greatest possible area. Since the area is given by L * W, we need to find the values of L and W that maximize this product while still satisfying the perimeter equation.
To find the dimensions, we can try substituting different values for L and solving for W. Starting with the given options, let's check each pair of dimensions:
1. For 16 feet by 20 feet:
L = 16
W = 20
Plugging these values into the perimeter equation, we get:
L + W = 16 + 20 = 36
The dimensions satisfy the perimeter equation, so let's calculate the area:
Area = L * W = 16 * 20 = 320 square feet
2. For 18 feet by 18 feet:
L = 18
W = 18
Plugging these values into the perimeter equation, we get:
L + W = 18 + 18 = 36
The dimensions satisfy the perimeter equation, so let's calculate the area:
Area = L * W = 18 * 18 = 324 square feet
3. For 14 feet by 22 feet:
L = 14
W = 22
Plugging these values into the perimeter equation, we get:
L + W = 14 + 22 = 36
The dimensions satisfy the perimeter equation, so let's calculate the area:
Area = L * W = 14 * 22 = 308 square feet
4. For 12 feet by 24 feet:
L = 12
W = 24
Plugging these values into the perimeter equation, we get:
L + W = 12 + 24 = 36
The dimensions satisfy the perimeter equation, so let's calculate the area:
Area = L * W = 12 * 24 = 288 square feet
Based on these calculations, the dimensions that give the greatest possible area are 18 feet by 18 feet, which would result in an area of 324 square feet.