perplexus.info :: Numbers : Appropriate Area

Appropriate Area (Posted on 2007-03-21)

Consider a triangle with sides of length 5, 6, 7. If you square the area of that triangle, you get 216, a perfect cube.

Are there other triangles (not geometrically similar to the first triangle) with integral sides whose area squared is a perfect cube? Find one such triangle, or prove no others exist.

No Solution Yet Submitted by Gamer

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Puzzle Thoughts

Comment 5 of 5 |

a=2r+1

b=r^2+r

c=r^2+ r+1

Then, the area is = r^3*(r+1)^3

For example, if r=3, we have: (a, b,c) = (7, 12,13).

Then, the area of the triangle is (3^3*4^3 = 12^3 = 1728

Thus, this pzrametric assignment results in an infinite number of triangles.

Posted by K Sengupta on 2023-03-16 02:32:42

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 (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info