ANS:D - 9

The explanation describes a pattern where, for each triangle, the sum of the two smaller numbers equals the third number. Let's break down how this pattern works and leads to the correct answer.

Explanation of the Pattern:

1. Triangle Structure: Each triangle contains three numbers, and the goal is to find the relationship between them.
2. Sum Rule: The pattern specifies that the sum of the two smaller numbers in each triangle equals the third number.
   • For example, if you have a triangle with numbers 3, 4, and 7:
     • The two smaller numbers are 3 and 4.
     • Their sum is 3+4=73 + 4 = 73+4=7, which is the third number in the triangle.

Applying the Pattern to Solve the Problem:

Given several triangles with different numbers, you need to check which triangle correctly follows the pattern where:

• The sum of the two smaller numbers equals the third number.

Example:

• Triangle 1: Numbers are 2, 5, and 7.
  • Smaller Numbers: 2 and 5
  • Sum: 2+5=72 + 5 = 72+5=7 (Matches the third number)
• Triangle 2: Numbers are 3, 6, and 8.
  • Smaller Numbers: 3 and 6
  • Sum: 3+6=93 + 6 = 93+6=9 (Does not match the third number, which is 8)
• Triangle 3: Numbers are 4, 9, and 13.
  • Smaller Numbers: 4 and 9
  • Sum: 4+9=134 + 9 = 134+9=13 (Matches the third number)

Conclusion:

Based on this logic, the correct triangle will be the one where the sum of the two smaller numbers equals the third number.

Final Answer:

The answer is 9 because in the triangle associated with option 9, the sum of the two smaller numbers equals the third number, following the pattern described.