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### 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/
```
Associated Topics:
High School Geometry
High School Triangles and Other Polygons

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