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.
This problem confused me. Any help??
perimeter = 36
so length + width = 18
so what length and width sum would get you 18 ?
l w Area
1 17 17
2 16 32
3 15 45
4 14 56
5 13 65
.....
9 9 81
notice that largest area is obtained when you create a square of 9 ft by 9 ft.
Of course! I can help you solve this problem step by step.
To find the areas of the different rectangles you can enclose with the given 36 feet of fencing, we need to consider the perimeter of a rectangle.
Let's start by understanding the formula for the perimeter of a rectangle. The perimeter of a rectangle is given by the formula: P = 2(l + w), where "l" represents the length and "w" represents the width of the rectangle.
In this case, since we have 36 feet of fencing, the perimeter should add up to 36 feet. So, we have the equation: 2(l + w) = 36.
Now, we need to find the possible combinations of whole-number values for length and width that satisfy the equation.
Let's list out some possible combinations:
1. If l = 1, then w = (36 - 2(1)) / 2 = 17. So, we have a rectangle with dimensions 1ft x 17ft, and the area is 1ft * 17ft = 17 square feet.
2. If l = 2, then w = (36 - 2(2)) / 2 = 16. So, we have a rectangle with dimensions 2ft x 16ft, and the area is 2ft * 16ft = 32 square feet.
3. If l = 3, then w = (36 - 2(3)) / 2 = 15. So, we have a rectangle with dimensions 3ft x 15ft, and the area is 3ft * 15ft = 45 square feet.
4. If l = 4, then w = (36 - 2(4)) / 2 = 14. So, we have a rectangle with dimensions 4ft x 14ft, and the area is 4ft * 14ft = 56 square feet.
5. If l = 5, then w = (36 - 2(5)) / 2 = 13. So, we have a rectangle with dimensions 5ft x 13ft, and the area is 5ft * 13ft = 65 square feet.
6. If l = 6, then w = (36 - 2(6)) / 2 = 12. So, we have a rectangle with dimensions 6ft x 12ft, and the area is 6ft * 12ft = 72 square feet.
7. If l = 7, then w = (36 - 2(7)) / 2 = 11. So, we have a rectangle with dimensions 7ft x 11ft, and the area is 7ft * 11ft = 77 square feet.
These are some examples of rectangles you can form with a perimeter of 36 feet, considering only whole-number dimensions. You can continue this process to find more combinations if needed.
I hope this explanation helps you solve the problem.