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.
(In reply to An idea
I've made an error in reasoning. The r I referred to doesn't have to be a whole number.
My reasoning that the bases of the triangles must in the reciprocal proportion to the heights is valid. Unfortunately the search as I did it is much harder.
EDIT: as shown by Steve Herman, the ratio of the bases is 44/45.
Edited on February 22, 2016, 10:44 am
Posted by Jer
on 2016-02-21 22:13:27