*Spoiler for New Scientist Enigma 1773 “Cutting Corners” *(Follow the link to see the puzzle.)

We need a triangle with one side 65 mm (we’ll work in millimeters to make everything an integer), another side *a*+*b*, and another side *c*+*d* such that the following are Pythagorean triples:

- 56,
*a*,*c*+*d* - 56,
*b*, 65 - 60,
*c*,*a*+*b* - 60,
*d*, 65

So immediately we have *b* = 33 and *d* = 25. Now we just scan a table of Pythagorean triples for ones with 56 as one leg and *a* as the other, where *a*+33 is the hypotenuse of a Pythagorean triple which has 60 as a leg. We find 56, 42, 70; 42+33 = 75 is the hypotenuse of the triple 45, 60, 75. So the triangle’s other two sides (in cm) are 7.0 and 7.5.

Is that all there is to it? Seems too easy.

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