If the two sides of the rectangle are labeled x and y, the the problem says that the perimeter P=100m, and that we are to make the area as large as possible. We have two variables in the problem, so we will use the perimeter information to eliminate one:
so
Now the area A is a function of x alone:
and we differentiate A(x) and set it equal to zero:
from which we deduce that y=25m. Hence, the rectangle is a square, of dimension 25mx25m.
