Talk:Largest Rectangle Contained in Triangle

In its current form, this page does not fully answer Dudeney's Puzzle 132.

There needs to be an argument shown that if the rectangle is simply contained, not inscribed, in the triangle, its area still cannot exceed half the area of the triangle.

This blog post, citing I. Niven, Maxima and Minima without Calculus (p. 58-61), does this by dividing the triangle into two parts with a line parallel to some side of the contained parallelogram.

I suggest creating a new page "Largest Parallelogram Contained in Triangle", moving the bulk of this proof there.

Then for this page, show that the midpoint method can create a rectangle half the area of the triangle, and link the new page to show the area is maximized.

--RandomUndergrad (talk) 03:52, 15 February 2022 (UTC)