All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Similar Sides Sought (Posted on 2005-06-20) Difficulty: 3 of 5
Find two similar triangles with sides (A,B,C) and (A,B,D), such that D-C=20141.

See The Solution Submitted by Old Original Oskar!    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Almost there... | Comment 4 of 6 |
It's clear that in the first triangle, C must be the smallest side, so that C≤A≤B; the second triangle must have A≤B≤D, and C/A=A/B=D/B.

If we call C/A=R, then A=CR, B=CR and D=CR, so D-C=C(R-1)=20141.

We can write C(R-1)=C(R-1)(R+R+1)=11x1831, so now we should try to equate terms... and that's as far as I got when I realized I would also have to prove that R was an integer.

  Posted by Federico Kereki on 2005-06-24 22:44:56
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information