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  1. MHB Apprentice
    Dhamnekar Winod's Avatar
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    #1
    Suppose, a rectangle circumscribes a quadrilateral having length of diagonals p and q, and area A.


    What is the maximum area of rectangle that circumscribes the given quadrilateral?










    Answer:-

    How to answer this question using geometry or calculus or by using both techniques.

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    #2
    Any other information about the "given" quadrilateral other than diagonal lengths, p and q, and area A?

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    #3
    If I can see correctly, no more information is needed. Just remember three details:

    - Area of a quadrilateral is $ \displaystyle A = \tfrac{1}{2}pq\sin \phi$, where $ \displaystyle p$ and $ \displaystyle q$ are the diagonal lengths and $ \displaystyle \phi$ the angle between the diagonals.

    - If you write a variable $ \displaystyle z$ as $ \displaystyle z = a + z - a$, nothing changes, but it might help solving considerably.

    - Zeros of the function derivative gives you the critical points inside a closed interval; end points you need to check by substituting.

    Hope this helps!

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