Select the missing number in the given diagrams:

Correct option is D

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Let's analyze the pattern in the given triangular diagrams.

We have the structure:

1. First triangle:

   • Top: 225
   • Bottom left: 8
   • Bottom right: 7

2. Second triangle:

   • Top: 49
   • Bottom left: 3
   • Bottom right: 4

3. Third triangle:

   • Top: 121
   • Bottom left: 6
   • Bottom right: ?

Identifying the pattern:

Observing the top numbers:

• 225 = 15²
• 49 = 7²
• 121 = 11²

Examining the bottom numbers:

• 8 × 7 = 56, which doesn’t directly relate to 225.
• 3 × 4 = 12, which doesn’t directly relate to 49.

However, the top numbers are squares of the sum of bottom numbers:

• (8 + 7)² = 15² = 225
• (3 + 4)² = 7² = 49
• (6 + ?)² = 11² = 121

Solving for ?:

• (6 + x)² = 121
• 6 + x = 11
• x = 5

Thus the correct answer  is option D) 5