Proper Integer Heronian Triangle whose Area is 24/Mistake

Source Work

1992: David Wells: Curious and Interesting Puzzles:

The Puzzles:

Bachet

$111$

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: $111$