Henry Ernest Dudeney/Puzzles and Curious Problems/203 - A Triangle Puzzle

Puzzles and Curious Problems by Henry Ernest Dudeney: $203$

A Triangle Puzzle

In the solution to our puzzle No. $162$, we said that:

"there is an infinite number of rational triangles composed of three consecutive numbers like $3$, $4$, $5$, and $13$, $14$, $15$."

We here show these two triangles.

In the first case the area ($6$) is half of $3 \times 4$,

and in the second case, the height being $12$, the area ($84$) is a half of $12 \times 14$.

It will be found interesting to discover such a triangle with the smallest possible three consecutive numbers for its sides,

that has an area that may be exactly divided by $20$ without remainder.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $203$. -- A Triangle Puzzle
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $269$. A Triangle Puzzle