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

by : $203$

 * 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.


 * Dudeney-Puzzles-and-Curious-Problems-203.png


 * 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.