Find range of values for a square's area. This is question is from my practice final exam.
The perimeter of a square is to be between 20 meters and 60 meters. What is the range of values for its area?

Hint: If a square has perimeter $P$ then, as each of its four edges must have the same length $l$, and the perimeter is the sum of the lengths of the edges, from $$P=4l$$ we get $$l=P/4.$$
We know that the area $A$ of a square with side-length $l$ is $A=l^2$.
Can you substitute the first equation $l=P/4$ into the second equation $A=l^2$ so that we have an equation relating the area $A$ and the perimeter $P$?
Now consider the value of the area if the perimeter is at its minimum $P=20$ and its maximum $P=60$.
