Perfect triangles are triangles with sides
of integer length and having numerically equal integer area and
perimeter.
A. Find Pythagorean Triangles (right triangles with integer
sides) that are Perfect Triangles.
B. Find all Perfect Triangles.
Some Discussion, Analysis,
and Solution Suggestions Note: A reader of this page has pointed out other
definitions of Perfect Triangle in the literature. This one is
commonly accepted. More general definitions (e.g. sides and area
are rational numbers) would lead to more sophisticated investigations.Reference:
Bonsangue, Martin V.; Gannon, Gerald E.; Buchman, Ed; &
Gross, Nathan. (1999). In Search of Perfect Triangles. Mathematics
Teacher, 92, 56-61.
The article traces the exploration of this problem by the
authors. There is a reference to our web site.
