Proper Integer Heronian Triangle whose Area is 24/Mistake
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Source Work
1992: David Wells: Curious and Interesting Puzzles:
- The Puzzles:
- Bachet
- $111$
- Bachet
Mistake
- What is the unique Heronian triangle with area $24$?
Correction
The fact that the only Heronian triangles under discussion are integer ones is implicit.
While the solution gives the solution $\tuple{ 4, 13, 15}$, the $\tuple {6, 8, 10}$ solution is overlooked.
Note, however, that this is a right triangle.
But it is indeed an integer Heronian triangle, just not a proper one.
Hence the question should be worded:
- What is the unique proper Heronian triangle with area $24$?
Sources
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Bachet: $111$