Problem of the Week: Cutting Up, Naturally

Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s).  Each week’s entries are scored by a faculty judge, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button.  The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.

Problem of the week

THE RULES:

The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited. Send solutions to bkennedy@gettysburg.edu. Weekly winners will receive a POW victory button, and the best-performing students of the semester will receive the Paul Mugabi problem-solving award. This problem was posted on Friday, September 3 and solutions are due on Friday, September 10 by 5:00 p.m.

THE PROBLEM: 

Suppose we have a square. We pick a point inside the square and use that point to make four triangles like this:

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Suppose that the four triangles each have different areas, and that the areas of all four triangles are positive whole numbers.

QUESTION: What is the smallest that the area of the original square can possibly be? Give the answer, and explain how you know.

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Author: Gettysburgian Staff

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