Question 570786: The perimeter of a rectangle is 2012, and lengths of all sides are integers. What is the smallest possible area of this rectangle? Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! If and are the dimensions of this rectangle, we know that so and
The area, as a function of x is
That quadratic equation represents a parabola.
Its axis of symmetry is
The maximum area occurs at , when the rectangle is a square.
Moving away from that point, to either side of , the area decreases.
Since the length of the sides are integers, the minimum will be for and , when one side measures 1 and the other 1005. It is the same solutionm no matter what side length we call x.
The minimum area is 1005.
