Select the triad in which the numbers are related to each other in the same way as the numbers in the following triads: 4-5-41 and 2-3-13. (Note: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)

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Let's analyze the given triads:

Given triads:
1) 4-5-41
2) 2-3-13

We need to find the relationship between the first two numbers and the third number.

Check the first triad:
4 and 5
Try to find a formula for the third number (41) using 4 and 5.

Check if 4^2 + 5^2 = 16 + 25 = 41
Yes, 41 = 4^2 + 5^2

Check the second triad:
2 and 3
2^2 + 3^2 = 4 + 9 = 13
Matches the third number 13.

So the relationship is: Third number = (First number)^2 + (Second number)^2

Now check the options:

1) 7-8-110
7^2 + 8^2 = 49 + 64 = 113 (not 110)

2) 10-11-211
10^2 + 11^2 = 100 + 121 = 221 (not 211)

3) 12-13-213
12^2 + 13^2 = 144 + 169 = 313 (not 213)

4) 5-6-61
5^2 + 6^2 = 25 + 36 = 61 (matches)

It seems option 4 matches the pattern perfectly.

Re-examining option 1:
7^2 + 8^2 = 49 + 64 = 113, which is close to 110 but not exact.

Therefore, the correct answer is option 4: 5-6-61.

Hence, the triad with the same relationship is 5-6-61.

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