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BayernBlues
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Homework Statement
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?
Homework Equations
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.