mrs. watterson wants to fence in an area for her dog. she has 72 feet of fencing and wants to use all of it to enclose a space with the greatest possible area. which dimensions will give her a space with the greatest possible area? (1 point)

16 feet by 20 feet
18 feet by 18 feet
14 feet by 22
12 feet by 24 feet

16 * 20 = 320 square feet

Multiply the others to find the that gives the largest number of square feet.

19*20=320

20

A. 16 by 20

Mr. Chambliss is planning to build a shed with a rectangular floor. In his original plan, the length of the floor was 7 feet and the area of the floor was 35 square feet. In his new plan, he wants to extend the length by 3 more feet. If the total area of the shed will be 70 square feet, by how many feet will he have to extend the width?

To find the dimensions that will give Mrs. Watterson the greatest possible area, we can use the formula for the area of a rectangle which is length multiplied by width.

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.