Henry Ernest Dudeney/Modern Puzzles/90 - Equal Perimeters
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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.
Click here for solution
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