1. The problem statement, all variables and given/known data The diagonals of a quadrilateral are perpendicular. The sum of the lengths of the diagonals is 6cm. What is the maximum area of such a quadrilateral? 2. Relevant equations 3. The attempt at a solution let x and y be the lengthes of the diagonals. Then the area of the quadrilateral is calculated by: a = ½ * x * y From the given conditions you know: x + y = 6 ==> y = 6 - x Plug in the term for y into the first equation: a(x) = ½*x*(6 - x) = -½x² + 3x I do not know what to do from here. I know that there is a graphing method but I'd rather do it through differentiation so could someone do the solution that way. The answer should be y=3 and x=3 so the dimensions are 3 x 3 I think.