Henry Ernest Dudeney/Modern Puzzles/90 - Equal Perimeters

by : $90$

 * Equal Perimeters
 * Rational right-angled triangles have been a fascinating subject for study since the time of, 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.