Susan has 50ft of fencing to use to build a garden in her backyard.

A: The shape must be a rectangle/square.

B: Sketch at least five different examples that Susan could use for her backyard and state what the perimeter of each one is.

C: The most important part, what is the largest area garden that Susan can create, show the garden's dimension and explain how you know it's the largest area.

P = 2L + 2W

All of the fencing must be 50 feet or less.

One dimension could be 7 by 18.

To determine the perimeter of different garden shapes, we need to consider the constraints given in the question: Susan has 50ft of fencing to use, and the shape must be a rectangle or square.

A: Since the shape must be a rectangle or square, we cannot consider shapes like circles or triangles.

B: Let's sketch at least five different examples of rectangle/square-shaped gardens, and calculate the perimeter of each:

Example 1: Square-shaped garden
If Susan decides to create a square-shaped garden, all sides will be equal in length. Let's assume each side of the garden has a length of x feet. Since there are four sides in a square, the perimeter will be 4x.

Example 2: Rectangular garden with equal sides
Another option is to have a rectangular-shaped garden with all sides equal in length. Let's assume each side of the garden has a length of x feet. The perimeter will be the same as that of a square, which is 4x.

Example 3: Rectangular garden with different length sides
Susan can also create a rectangular garden where the length and width are not equal. Let's assume the length is x feet and the width is y feet. The perimeter of this rectangular garden will be 2x + 2y.

Example 4: Narrow rectangular garden
In this case, Susan decides to have a long and narrow rectangular garden. Let's assume the length is x feet, and the width is y feet. The perimeter will be 2x + 2y.

Example 5: L-shaped garden
Susan can also create an L-shaped garden with a rectangular section and an additional rectangular strip attached to it. Let's assume the length of the rectangular section is x feet, and the width of both sections is y feet. The perimeter will be 2x + 3y.

C: To find the largest area garden, we need to compare the areas of the different shapes. The formula for the area of a rectangle is length times width, while for a square, it's side multiplied by side.

To determine the largest area, we can calculate the area for each shape based on the given perimeters:

1. Square-shaped garden: Area = x * x = x^2
2. Rectangular garden with equal sides: Area = x * x = x^2
3. Rectangular garden with different length sides: Area = x * y
4. Narrow rectangular garden: Area = x * y
5. L-shaped garden: Area = x * y

By comparing the areas of the different gardens, we can select the shape that yields the largest area.