There are two rectangles 1 × 2 and 3 × 4 with parallel sides centered at a common point O. Points F and G are selected on the boundary of the inner and outer rectangle, respectively. What is the maximum possible area of triangle FOG?
(In reply to
Solution by Jer)
I'm not clear on what three points you are choosing for the triangles.
Consider just the second case where 1 and 4 are parallel:
Say the center of each rectangle is at (0,0) each rectangle has one vertex in each quadrant.
In Quadrant I, the inner rectangle's vertex is (1/2, 1) and the outer triangle's is (2, 1.5).
One of the triangle's vertices has to be at (0,0), the "O" in "triangle FOG". The area of the large rectangle is 12; I'm not seeing how any triangle with (0,0) as one of its vertices can have an area as large as 6.
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Posted by Larry
on 2024-12-12 08:37:16 |