Find a pair of triangles, one is a right triangle and one is an isosceles triangle, subject to the following conditions:
1) Both triangles have integer sides.
2) Both triangles have the same perimeter
3) Both triangles have the same integer area.

To solve this requires, among other things, whole numbers a,b,c,d,r such that
r>1
a^2+b^2=c^2
a^2+b^2*r^4=d^2

A search employing Euclid's formula a=m^2-n^2, b=2mn gives a solution (the only one with m<52, n<100, r<10)
of m=51, n=14, r=9
so that
a=2405, b=1448, c=2793, d=115993

this particular set of numbers does not lead to a solution of the problem though.

Posted by Jer on 2016-02-20 16:18:39