
06520661
j
2016a.00619
Palfreyman, Andrew
Equable triangles  the general case.
SYMmetryplus 57, 57 (2015).
2015
Mathematical Association (MA), Leicester
EN
G40
G70
G30
F60
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
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.