The problems on this page involve *many* mathematical relationships. The thing
they have in common is that the
Pythagorean Theorem is utilized in the solution, *but
it is not obvious at first glance *to
use the Pythagorean Theorem. Below is my criteria for problems
on this page.

A rectangular box is tied with a ribbon so that the ribbon crosses the box at the midpoints of its sides. If the box is 8 inches long, 6 inches wide, and 5 inches high, how long is the ribbon? (This problem from |

What is the length of the shortest string that can stretch from point X to point Y along the outside of the box in the diagram? (The dimensions are in inches.) (This problem from |

Three balls are placed inside a cone such that each ball is in contact
with the edge of the cone and the next ball. If the radii of the balls
are 20 cm, 12 cm, and r cm respectively, what is the value of r? (This problem from www.mathschallenge.net.). |

Problems I have selected to put on this page meet the following criteria:

- The problem is a good problem-solving problem.
- It utilizes the Pythagorean Theorem in the solution,
*but it is not obvious at first glance*to use the Pythagorean Theorem. - The problem involves mathematical (often geometric) properties other than
just the Pythagorean Theorem. It is worth noting that the aspect that make
many
of
these problems challenging is
*not*the Pythagorean Theorem.

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James R. Olsen, Western Illinois University

E-mail: `jr-olsen@wiu.edu`

*Page last updated:*
February 12, 2004