Answer:
The dimensions are 50 and 100 square foot
Step-by-step explanation:
Let x = length of fenced side parallel to the side that borders the playground
y = length of each of the other two fenced sides
Then, x + 2y = 200
<=> x = 200-2y
The Area = xy = y(200-2y)
The dimensions of the playground that will minimize the homeowner's total cost for materials when the area of the playground is maximum. He can cover more area but with the same cost.
The graph of the area function is a parabola opening downward.
The maximum area occurs when y = -200/[2(-2)] = 50
=> x = 100
So the dimensions are 50 and 100 square foot
Except x+12=5x-2
because:
4+12= 5*4-2
16=20-2
16=18 -- which is not true
32, 38, so on. So its +4 then +8 then +12 +16 +20....
