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A Problem to Ponder Throughout the Summer

As a way to belay her grading of exams, MJ (Bellingham) sent the following "Problem to Ponder" via an e-mail to multiple people....

"...here are a couple of questions I was pondering about the triangles above. They are not quite to scale but close.

Be sure to make an intuitive guess before you start cranking.

Questions:

  1. Which is closer to being "equilateral"?
  2. Which has more area?
  3. Any other questions you want to ask, such as what is the ratio of the areas, etc.?
  4. For what grade level is this appropriate?
Back to my exams."

Hint

Commentary on solutions to problems is available only after a problem is placed in the website's archive. If your students (or you) have interesting solutions or insights relative to these problems, please send them to the Math Partnership Project, c/o Jerry Johnson, Western Washington University, Bellingham, WA 98225-9063. All submissions will be considered for inclusion as part of the commentary in the archive section.