# 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: $111$