harris is planting a rectangular garden with an area of 24 square. he is also putting a fence around his garden. how should he arrange his garden so he can buy the least amount of fence possible?
To determine how Harris should arrange his garden to minimize the amount of fence he needs, we need to consider the factors that will affect the perimeter of the garden.
First, let's think about the possible dimensions of the rectangular garden. The area of the rectangular garden is given as 24 square units. We can find the dimensions of the rectangular garden by finding the factors of 24. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Next, let's calculate the perimeter for each possible dimension. The perimeter of a rectangle is given by the following formula:
Perimeter = 2(length + width)
We can calculate the perimeters for each possible dimension:
For length = 1 and width = 24:
Perimeter = 2(1 + 24) = 50
For length = 2 and width = 12:
Perimeter = 2(2 + 12) = 28
For length = 3 and width = 8:
Perimeter = 2(3 + 8) = 22
For length = 4 and width = 6:
Perimeter = 2(4 + 6) = 20
For length = 6 and width = 4:
Perimeter = 2(6 + 4) = 20
For length = 8 and width = 3:
Perimeter = 2(8 + 3) = 22
For length = 12 and width = 2:
Perimeter = 2(12 + 2) = 28
For length = 24 and width = 1:
Perimeter = 2(24 + 1) = 50
By comparing the perimeters, we can see that the least amount of fence required will be when Harris arranges his garden with dimensions of 4 units for length and 6 units for width. Thus, his garden should have dimensions of 4 units by 6 units to minimize the amount of fence needed.
The possible dimensions could be
4 by 6 with a perimeter of 20
3 by 8 with a perimeter of 25
2 by 12 with a perimeter of 28