You have 500 ft of fencing all rolled up and you want to make a rectangular playground area for your son. What are the dimensions of the largest playground you could build?

Question

anonymous · Answer

Start with the perimeter:
500 = 2*base+2*height
250 = base+height
base = 250 - height

Therefore:
Area = (250-height)*height
Area = (250 - height)(height)
Area = 250*height - height^2

When the derivative is 0, there is a maximum or a minimum:
dA/dh = 250 - 2*height
0 = 250 - 2*height
height = 125

To confirm this is a maximum, check that the second derivative is negative:
d2A/d2h = -8

Therefore, this is a maximum.
height = 125
base = 250 - height
base = 125

Largest playground: 125x125

anonymous · Answer

@awesomeb woah,, a lot of stuff lol thanks :) If you don't mind, could you help me with another similar problem like this please? >.<"

anonymous · Answer

yes make a new problem and tag me

anonymous · Answer

@awesomeb Okay :) I really appreciate it! ^-^

anonymous · Answer

np