
MHB Apprentice
#1
January 16th, 2020,
08:42
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.

January 16th, 2020 08:42
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MHB Journeyman
#2
Yesterday,
16:00
Any other information about the "given" quadrilateral other than diagonal lengths, p and q, and area A?

MHB Apprentice
#3
Yesterday,
20:49
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!