\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016a.00619}
\itemau{Palfreyman, Andrew}
\itemti{Equable triangles -- the general case.}
\itemso{SYMmetryplus 57, 5-7 (2015).}
\itemab
From the text: A shape was said to be equable in my last two articles if the value of its area is equal to the value of its perimeter and I was particularly interested in shapes that had integers for all their side lengths. In the previous article, however, we found that no equable isosceles triangle exists, although a nice example did exist with a base of $12$ and equal sides being $7\frac{1}{2}$. We will now consider the general case for a triangle which has a slightly different approach to that in the last article. However, we will begin with Heron's formula again.
\itemrv{~}
\itemcc{G40 G70 G30 F60}
\itemut{equable shapes; equable triangles; Heronian triangles; integer side length; integer area; Herons's formula; Pythagorean triples; Diophantine equations; inequalities; case analysis; analytic geometry; plane geometry}
\itemli{}
\end