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Matching Isosceles and Right Triangle (Posted on 2016-02-19) Difficulty: 4 of 5
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.

See The Solution Submitted by Brian Smith    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: An idea | Comment 5 of 7 |
(In reply to An idea by Jer)

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

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