134k views
5 votes
A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular. Part I: For any given perimeter P, the rectangle that encloses the greatest area is a square. Write an equation for the area, A, in terms of the perimeter P, and the side length x. Part II: Use the equation from Part I to result to write a simple equation to find the least amount of fencing necessary for a playground with an area of 256 square yards.

User Brickingup
by
8.7k points

1 Answer

3 votes
Considering the playground to be a square:
Perimeter = x + x + x + x
P = 4x

Area = x²

Px = 4x²
x² = Px/4
Area = Px/4

The fencing will be equal to the perimeter, with area 256 sq yd
256 = Px/4
P = 1024 / x
User Stantonk
by
7.4k points