If you have 36ft of fencing what are the areas of the different rectangles you could enclose with the fencing? Consider only whole number dimensions.
2 * 18
3 * 12
4 * 9
6 * 6
There are many different areas
1+ 1+17 + 17= 36
1 times 17 = 17
9 + 9 + 9 + 9 = 36
9 times 9 = 81
Look for possibilities between these two.
To find the different areas of rectangles that can be enclosed with 36 ft of fencing, we need to consider the perimeter of a rectangle.
The perimeter of a rectangle can be calculated by adding the lengths of all four sides. In this case, the perimeter of each rectangle is given as 36 ft.
Let's start with the first possible scenario where the length is 1 ft. In this case, the remaining fence length is 36 - 1 - 1 = 34 ft. Since the perimeter is 36 ft, the other side will also have a length of 17 ft. Thus, the area of this rectangle is 1 ft * 17 ft = 17 sq ft.
Next, let's consider the scenario where the length is 2 ft. The remaining fence length is 36 - 2 - 2 = 32 ft. Since the perimeter is 36 ft, the other side will also have a length of 16 ft. The area of this rectangle is 2 ft * 16 ft = 32 sq ft.
We can continue this process for different length dimensions until the remaining fence length becomes negative or zero.
Here are the different rectangles that can be formed along with their areas:
- Rectangle with length = 1 ft and width = 17 ft (Area = 1 ft * 17 ft = 17 sq ft)
- Rectangle with length = 2 ft and width = 16 ft (Area = 2 ft * 16 ft = 32 sq ft)
- Rectangle with length = 3 ft and width = 15 ft (Area = 3 ft * 15 ft = 45 sq ft)
- Rectangle with length = 4 ft and width = 14 ft (Area = 4 ft * 14 ft = 56 sq ft)
- Rectangle with length = 5 ft and width = 13 ft (Area = 5 ft * 13 ft = 65 sq ft)
- Rectangle with length = 6 ft and width = 12 ft (Area = 6 ft * 12 ft = 72 sq ft)
- Rectangle with length = 7 ft and width = 11 ft (Area = 7 ft * 11 ft = 77 sq ft)
- Rectangle with length = 8 ft and width = 10 ft (Area = 8 ft * 10 ft = 80 sq ft)
- Rectangle with length = 9 ft and width = 9 ft (Area = 9 ft * 9 ft = 81 sq ft)
These are the different rectangles that can be enclosed with 36 ft of fencing, considering only whole number dimensions.