perplexus.info :: Just Math : Take five

Take five (Posted on 2011-05-22)

A triangle is Heronian if all its sides and its area are integers.
Any such rational triangle can be scaled up to a corresponding triangle with integer sides and area, and often the term Heronian triangle is used to refer to the latter.
There are only 5 Heronian triangles (with all sides being integers) whose perimeters numerically are equal to their areas.

You are requested to find all of them.

Submitted by Ady TZIDON

Rating: 3.6667 (3 votes)

Solution: (Hide)

1. ( 6, 8, 10) Area = Perimeter = 24
2. ( 5, 12, 13) Area = Perimeter = 30
3. ( 9, 10, 17) Area = Perimeter = 36
4. ( 7, 15, 20) Area = Perimeter = 42
5. ( 6, 25, 29) Area = Perimeter = 60
Copied from Dej Mar's solution

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Rest time over	Dej Mar	2011-05-22 17:55:57
Left triangles	Math Man	2011-05-22 15:30:15

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 (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info