10.
Find a third number so that the three numbers form a right triangle:
i)
9, 41

Step-by-step explanation:

There are two possibilities here:

1) The two numbers are the legs of the right triangle. Then the hypotenuse is ...

  √(9^2 +41^2) = √1762 ≈ 41.9762

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2) The length 41 is the hypotenuse. Then the other leg is ...

  √(41^2 -9^2) = √1600 = 40

Comment on Pythagorean triples

I find it somewhat interesting that for any odd number n, one Pythagorean triple involving that number is ...

  (n, (n^2 -1)/2, (n^2 +1)/2)

For n=9, the triple is (9, 80/2, 82/2) = (9, 40, 41).

Along these lines, ones commonly seen in math problems are ...

  (3, 4, 5), (5, 12, 13), (7, 24, 25), (9, 40, 41), (11, 60, 61)

10000

step-by-step explanation: divide by 2,