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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.)
An idea | Comment 4 of 7 |
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
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