Mariah has a flower bed that is 10 feet long and 5 feet wide. She wants to put a fence around the flower bed to keep the deer from eating her flowers. She also wants to leave enough space to walk between the fence and the flower bed. What is the perimeter of the fence if the space between the flower bed and fence is represented by x?
you have to add x on each side, or 2x to both dimensions. So the perimeter is
2(5+2x+ 10+2x) = 30+8x
To find the perimeter of the fence, we need to add up the lengths of all four sides.
The flower bed is 10 feet long and 5 feet wide. Let's label the length as L and the width as W.
The length of the fence on one side will be: L + 2x
The length of the fence on the adjacent side will also be: L + 2x
The length of the fence on the other two sides, which are the widths, will be: W + 2x
To find the perimeter, we add all four sides:
Perimeter = (L + 2x) + (L + 2x) + (W + 2x) + (W + 2x)
Simplifying,
Perimeter = 2L + 2W + 4x
Given that the flower bed is 10 feet long and 5 feet wide, L = 10 and W = 5. Substituting these values,
Perimeter = 2(10) + 2(5) + 4x
Perimeter = 20 + 10 + 4x
Perimeter = 30 + 4x
Therefore, the perimeter of the fence, with the space between the flower bed and fence represented by x, is 30 + 4x feet.
To find the perimeter of the fence, we need to calculate the total length of all four sides.
First, let's consider the length of the two sides that are 10 feet long. Since we need to leave enough space for walking between the flower bed and the fence, we should add the space on both sides of the bed. So each 10-foot side will have a space of x feet on one side and x feet on the other, resulting in a total length of 10 + x + x = 10 + 2x.
Next, let's consider the width of the flower bed, which is 5 feet. Similarly, we need to add the space on both sides, so each 5-foot side will have a space of x feet on one side and x feet on the other, resulting in a total length of 5 + x + x = 5 + 2x.
The total perimeter of the fence will be the sum of all four sides, which are (10 + 2x) + (5 + 2x) + (10 + 2x) + (5 + 2x). Simplifying this expression, we get 30 + 8x.
Therefore, the perimeter of the fence, represented by 30 + 8x, where x is the space between the flower bed and the fence.