Cynthia wants to design a rectangular playground of 616 square metres and she also wants to have a fence built around it. However, she only has enough fence materials for a playground of 100 metres in perimetre. What should be the dimensions of the playground?
+23251 To create a rectangular playground with a perimeter of 100 metres and an area of 616 square metres:
Call the length: l
Call the width: w
Since the perimeter is 100: 2l + 2w = 100 ---> l + w = 50
Since the area is 616: l · w = 616
Solve l + w = 50 for l: l = 50 - w
Replace this into the area equation: l · w = 616 ---> (50 - w) · w = 616 ---> 50w - w2 = 616
---> 0 = w2 - 50w + 616 ---> w2 - 50x + 616 = 0
Factoring: (w - 22)(w - 28) = 0
So: either w = 22 or w = 28
If w = 22, then l = 28 or if w = 28, then l = 22.
In either case, the dimensions of the playground are: 22 metres x 28 metres.
