The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 2 square flower beds, one on each side of the playground. The length of the playground is l and its width is w. The length of each side of the flower beds is a. Which two equivalent expressions represent the total fencing material required to surround the playground and flower beds? Assume that the playground and beds do not overlap.
h flower beds is or .
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What expressions?
2(4a) + 2l + 2w
The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 2 square flower beds, one on each side of the playground. The length of the playground is l and its width is w. The length of each side of the flower beds is a. Which two equivalent expressions represent the total fencing material required to surround the playground and flower beds? Assume that the playground and beds do not overlap.
To find the total fencing material required to surround the playground and flower beds, we need to calculate the perimeter of each element and then add them together.
The perimeter of a rectangle (playground) is given by the formula: 2(length + width).
Therefore, the perimeter of the playground is: 2(l + w).
The perimeter of a square (flower bed) is given by the formula: 4(side length).
Therefore, the perimeter of each flower bed is: 4a.
Since there are two flower beds, the total perimeter of the flower beds is: 2 * 4a = 8a.
To find the total fencing material required, we need to add the perimeters of the playground and the flower beds:
Total fencing material = Perimeter of playground + Perimeter of flower beds
Total fencing material = 2(l + w) + 8a
Therefore, the two equivalent expressions that represent the total fencing material required are:
1. 2(l + w) + 8a
2. 8a + 2(l + w)