Question

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?

Answer 1

The largest area would be a square with 125 ft of fencing on each side.

Hope this helps

Answer 2

The answer Fam Is..........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