text: help plz   the perimeter of a rectangle is 18cm. whats its greatest possible area? plz help me for the first, if one side is x, then another side would be 9-x (so that they would add up to 18).  the area is then  a = x(9-x) = 9x - x^2  to find the maximum area, take the first derivative and set it to 0:  a' = 9 - 2x 0 = 9 - 2x 2x = 9 x = 9/2  since the parabola opens down, the maximum area happens when x = 9/2.  so if x = 9/2, the other side is 9 - 9/2, or 9/2 - it turns out to be a perfect square!  and the area is then (9/2)^2, or 81/4.