id: 06520661
dt: j
an: 2016a.00619
au: Palfreyman, Andrew
ti: Equable triangles ‒ the general case.
so: SYMmetryplus 57, 5-7 (2015).
py: 2015
pu: Mathematical Association (MA), Leicester
la: EN
cc: G40 G70 G30 F60
ut: 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
ci:
li:
ab: 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.
rv: