You have 24 feet of fence to make a rectangular garden.Each side will measurw a whole number of feet.How many different sized rectangular gardens can you make?
To find out how many different sized rectangular gardens you can make with 24 feet of fence, we need to consider the perimeter of the rectangle.
Let's use the formula for the perimeter of a rectangle:
Perimeter = 2 * (Length + Width)
Since the length and width need to be whole numbers, we can start by trying different values for one side (either length or width) and calculate the other side.
First, let's consider the length. Since the perimeter is 24 feet, the maximum value for the length would be half of the perimeter (12 feet). Let's calculate the corresponding width for each length:
For a length of 1 foot: Width = 24 - 2 * 1 = 22 feet
For a length of 2 feet: Width = 24 - 2 * 2 = 20 feet
For a length of 3 feet: Width = 24 - 2 * 3 = 18 feet
For a length of 4 feet: Width = 24 - 2 * 4 = 16 feet
For a length of 5 feet: Width = 24 - 2 * 5 = 14 feet
For a length of 6 feet: Width = 24 - 2 * 6 = 12 feet
As we can see, for each length from 1 to 6 feet, we have a corresponding width. Therefore, we can create 6 different sized rectangular gardens using 24 feet of fence.
To summarize, there are 6 different sized rectangular gardens that can be made with 24 feet of fence.
To find out how many different sized rectangular gardens you can make with 24 feet of fence, you need to consider all the possible dimensions.
Let's start by listing all the possible lengths of the gardens. Since each side of the garden must be a whole number of feet, the maximum length you can have is half of the total fence length. In this case, the maximum length you can have is 12 feet.
Now, let's go through all the lengths from 1 to 12 and find the corresponding widths that result in a perimeter of 24 feet.
Length: 1 ft, Width: 11 ft (1 + 11 + 1 + 11 = 24)
Length: 2 ft, Width: 10 ft (2 + 10 + 2 + 10 = 24)
Length: 3 ft, Width: 9 ft (3 + 9 + 3 + 9 = 24)
Length: 4 ft, Width: 8 ft (4 + 8 + 4 + 8 = 24)
Length: 5 ft, Width: 7 ft (5 + 7 + 5 + 7 = 24)
Length: 6 ft, Width: 6 ft (6 + 6 + 6 + 6 = 24)
So, you can make 6 different sized rectangular gardens with 24 feet of fence.
24/4 = 6
P = 2L + 2W
Your garden could be 6 feet by 6 feet.
It could be 5 by 7.
What other measurements can you think of?