Jose wants to put fencing around his rectangular garden. His garden measures 31 feet by 33 feet. The garden has a path around it that is 3 feet wide. How much fencing does Jose need to enclose the garden and path?
I need help
To calculate the amount of fencing Jose needs, we need to find the perimeter of the garden and the path.
The garden measures 31 feet by 33 feet. Since there are two pairs of sides that are equal in length, we can calculate the perimeter using the formula: perimeter = 2 * (length + width).
Perimeter of the garden = 2 * (31 + 33)
Perimeter of the garden = 2 * 64
Perimeter of the garden = 128 feet
The path around the garden is 3 feet wide, which means that each dimension of the garden will be increased by 3 feet on all sides.
The new dimensions of the garden will be (31 + 2 * 3) feet by (33 + 2 * 3) feet.
The new dimensions of the garden will be 37 feet by 39 feet.
Now, to find the perimeter of the entire area (garden + path), we use the same formula as before.
Perimeter of the entire area = 2 * (length + width)
Perimeter of the entire area = 2 * (37 + 39)
Perimeter of the entire area = 2 * 76
Perimeter of the entire area = 152 feet
So, Jose needs 152 feet of fencing to enclose both the garden and the path.
To calculate the amount of fencing Jose needs for his garden and the path, we need to find the perimeter of the outer boundary.
First, let's calculate the perimeter of the garden. The formula to find the perimeter of a rectangle is given by:
Perimeter = 2 * (Length + Width)
Here, the length of the garden is 31 feet and the width is 33 feet. Plugging these values into the formula:
Perimeter of garden = 2 * (31 + 33) = 2 * 64 = 128 feet.
Now, let's calculate the perimeter of the outer boundary, which includes the garden and the path around it. Since the path is 3 feet wide, we need to increase the length and width of the garden by 6 feet (3 feet on each side). The new length and width will be:
New length = Length + 2 * Path Width
= 31 + 2 * 3
= 31 + 6
= 37 feet
New width = Width + 2 * Path Width
= 33 + 2 * 3
= 33 + 6
= 39 feet
Now we can calculate the perimeter of the outer boundary by using the same formula as before:
Perimeter of outer boundary = 2 * (New length + New width)
= 2 * (37 + 39)
= 2 * 76
= 152 feet.
Therefore, Jose needs 152 feet of fencing to enclose the garden and path.
With the path, the dimensions are 37 by 39.
P = 2L + 2W