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2011 AIME A #8: Triangular Tables

Foam Table 1I was inspired to have some more fun with folding by a question from this year’s American Invitational Mathematics Examination (AIME) that turned triangles into tables and asked “How high can the table go?”.  (You can find the question here).

Investigating the problem seemed like more fun than solving it, so I cut out a triangle from some foam board and scored lines near the vertices.

Foam Triangle 2

Then I folded the corners and made the following table with an irregular hexagonal top!

Foam Fold

I made a few, to see what kinds of heights I could get.

Foam Tables

There are so many fun questions to explore here!  What comes to mind?

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One Comment

  1. Matt Skoss says:

    This would make an interesting investigation for students to explore…range of exit points…Year 3 through to 12.

    I’d probably start with an equilateral triangle with younger kids, and move to an isosceles or scalene with older kids.

    It’s a bit artificial lack in a context, but a challenge could be to have a ratio of the area of the top to the height as 1:1 (ignoring the units, like when considering surface area to volume ratio).

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