If the area of rectangle $ABCD$ with integral sides is $48$ sq.cm. If $E$ be any point on AD. How to find the sum of maximum and minimum area (sq.cm) of $\triangle BCE$?
How to find the sum of maximum and minimum area of a triangle within a rectangle?
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geometry
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0@André Nicolas:Aha yes I forgot to add the "same base" constraint.and please feel free to edit the answer further based on your understanding,I would never doubt it:) – 2011-10-21
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Assuming the usual clockwise or anticlockwise notations.
Since we know that the areas of two or more triangle having the same base and lying between the same parallel lines will be equal, so here we would have equal maximum and minimum area for $\triangle BCE$.
Again, the area of a triangle is given by $\frac{1}{2}\times x \times y$ where $x$,$y$ are the sides of rectangle. Here the constraint is $x \times y = 48 $ sq.cm. So choosing any value of $x,y$ satisfying this constraint would give the same area for any $\triangle BCE$.
Hence, in this case, the maximum area + minimum area = $48$ sq.cm.
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3I think you can even post it as a non-CW answer. The site explicitly permits (and encourages?) that. – 2011-10-21