# Problem of the Week: Mesmerized by Measurement

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.

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. This problem was posted on Friday, March 8 and solutions are due on Friday, April 15 by 5:00 p.m.

THE PROBLEM:

Suppose that a rectangle’s longest side is s meters. (Maybe all sides are of length s meters, but no side is longer than s meters.) Suppose that the rectangle’s area is A square meters, and that the rectangle’s perimeter is P meters.

QUESTION: If A = P, what can you say about s? Explain.

Author: Phoebe Doscher

Phoebe Doscher ’22 is the Editor-in-Chief of The Gettysburgian. She formerly worked as Magazine Editor, News Editor, Assistant News Editor, Staff Writer, and Copyeditor. She is an English with a Writing Concentration and Theatre Arts double major. On campus, she is an intern for Gettysburg’s Communications & Marketing Office, the president of the Owl & Nightingale Players, and the News Director for WZBT, serving as the co-host of The Gettysburgian’s podcast On Target.