How Long is the Hypotenuse?

Date: 07/12/99 at 11:10:34
From: Jon Mann
Subject: Geometry Question

In a right triangle, the lengths of the segments connecting the points 
of trisection of the hypotenuse to the vertex of the right angle are 7 
and 9. How long is the hypotenuse of the triangle?

Also, what are some generalizations that I can make about this sort 
of problem?

Thank you.

Date: 07/12/99 at 12:56:54
From: Doctor Peterson
Subject: Re: Geometry Question

Hi, Jon.

If you draw segments from each trisection point parallel to the legs, 
you get something like this:

       +
       |\
      a| \c
       |  \
       +---*
       |  /|\
      a| 9/| \c
       | / |  \
       +-/-+---*
       |/  | / |\
      a|/  /7  | \c
       / / |   |  \
       +---+---+---+
         b   b   b

You have a lot of congruent right triangles with sides a, b, and c, 
and two interesting ones with hypotenuse 7 and 9. Write the 
Pythagorean Theorem for each of these, and see what it tells you! 
Then see what happens if 7 and 9 are replaced by any other numbers.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/