Rhombus Problem (Maximum Area)

Geometry Level 3

What is the greatest possible area for a rhombus constructed on a 3 m × 9 m \text{3 m} \times \text{9 m} sheet of paper? Give your answer in m 2 \text{m}^2 .


The answer is 15.

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1 solution

Douglas Foster
Dec 19, 2019

Here is my math to show it

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How do we know this is maximal?

Richard Desper - 1 year, 5 months ago

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not sure if i have the chops for a full proof, but using area = (pq)/2 where p and q are the diagonals, you know you have to maximize pq. I'm not sure exactly how to prove it, but any other combination of corners make diagonals that multiply to less than 30. Maybe if I have some free time or a new idea for how to do it I will update this post.

Douglas Foster - 1 year, 5 months ago

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well, you're clearly maximizing the length of the longer diagonal. Halfway home!

Richard Desper - 1 year, 5 months ago

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