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.
The total fencing material required to fence the playground and both flower beds is
or
.
Which what? No expressions given.
To determine the total fencing material required to surround the playground and flower beds, we need to calculate the perimeter of each component and add them together.
1. Perimeter of the Playground:
The perimeter of a rectangle is given by the formula P = 2l + 2w. Therefore, the perimeter of the playground is 2l + 2w.
2. Perimeter of a Square Flower Bed:
The perimeter of a square can be calculated by multiplying the length of one side by 4. Hence, the perimeter of one square flower bed is 4a.
Since there are two flower beds, the total perimeter for both of them is 2 * 4a = 8a.
Therefore, the total fencing material required to surround the playground and both flower beds is equal to the sum of the perimeters of the playground and the flower beds:
Total fencing material required = Perimeter of the Playground + Perimeter of the Flower Beds
= 2l + 2w + 8a
Hence, the two equivalent expressions that represent the total fencing material required are:
2l + 2w + 8a or 8a + 2l + 2w