Henry Ernest Dudeney/Modern Puzzles/90 - Equal Perimeters

Modern Puzzles by Henry Ernest Dudeney: $90$

Equal Perimeters

Rational right-angled triangles have been a fascinating subject for study since the time of Pythagoras, before the Christian era.

Every schoolboy knows that the sides of these, generally expressed in whole numbers,

are such that the square of the hypotenuse is exactly equal to the sum of the squares of the other two sides.

Now, can you find $6$ rational right-angled triangles each with a common perimeter, and the smallest possible?

It is not a difficult puzzle like my "Four Princes" (in the Canterbury Puzzles), in which you had to find four such triangles of equal area.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $90$. -- Equal Perimeters
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $173$. Equal Perimeters