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

Home > Shapes > Geometry
Equal Areas and Perimeters (Posted on 2007-01-02) Difficulty: 3 of 5
The rectangle with length 6 and width 2 has the same perimeter and area as the triangle whose sides have lengths 5, 5, and 6.

Is there a triangle with the same perimeter and area as the rectangle that has length 3 and width 2 ? If so, find the lengths of its three sides. If not, explain why not.

See The Solution Submitted by Dennis    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution Comment 1 of 1

The perimeter would be 10 and the area would have to be 6.

The triangle with a given perimeter would have the maximum area if the sides were all the same length--an equilateral triangle.  In this case each side would be 10/3. Its height would be 10sqrt(3)/6, and its area would be 100sqrt(3)/36 ~= 4.811252243246881. No way of rearranging the sides would make it any larger in area, so it could not get up to 6.


  Posted by Charlie on 2007-01-02 13:50:19
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information