Answer: it is well known that the largest area would be a circle with circumference 120 ft, and it is well known that a square 30ft on a side gives the most area of all retangles with perimeter 120 ft, but we are to prove it. The equation is area = side × (60 - side).
Step-by-step explanation:
Let s be one side of the rectangle, and 60-s be the other side. Maximize the area, which is
a(s) = s×(60-s) = -s^2 + 60s
This quadratic equation reaches a maximum when da(s)/ds = 60 - 2s = 0.
2s = 60, s = 30.
