To solve this problem, we need to identify the pattern and calculations involved in the given equations and apply the same logic to the third equation.

Let's analyze the given pattern:

1. \(36 \, \square \, 81 = 6; 9; 15\)
2. \(64 \, \square \, 144 = 8; 12; 20\)

From the above equations, we observe:

• The numbers \(6\) and \(8\) are derived from the square root of the first number: \(\sqrt{36} = 6\), \(\sqrt{64} = 8\).
• The numbers \(9\) and \(12\) are derived from the square root of the second number: \(\sqrt{81} = 9\), \(\sqrt{144} = 12\).
• The numbers \(15\) and \(20\) are the sums of these roots: \(6 + 9 = 15\), \(8 + 12 = 20\).

Now, applying the same pattern to the third equation:

1. \(49 \, \square \, 100 = ?\;;\;?\;;\;?\)

• Calculate the square root of \(49\): \(\sqrt{49} = 7\).
• Calculate the square root of \(100\): \(\sqrt{100} = 10\).
• Sum these roots: \(7 + 10 = 17\).

Thus, the solution to the third equation is 7; 10; 17.

This matches the given correct answer 7; 10; 17.