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The first triangle has 108 at the top and 9 and 12 at the bottom.

Mathematics

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Step-by-step solution

3 steps

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  1. Analyze the first example.

    The first triangle has 108 at the top and 9 and 12 at the bottom.
    We observe that the product of the two bottom numbers equals the top number:

    9×12=1089 \times 12 = 108
  2. Analyze the second example.

    The second triangle has 108 at the top and 9, 12, and 12 at the bottom.
    Applying the same pattern from Step 1, we take the product of the first two bottom numbers:

    9×12=1089 \times 12 = 108

    This matches the top number. The third number (12) at the bottom right is not used in this pattern.

  3. State the general rule.

    The pattern demonstrated by these examples is that the number at the top of the triangle is the product of the two numbers in the bottom-left and bottom-center positions.

    The rule is: Top Number=Bottom Left Number×Bottom Center Number\boxed{\text{Top Number} = \text{Bottom Left Number} \times \text{Bottom Center Number}}

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