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Finding the Third Proportional to 102.09 and 217.13

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Solution

The third proportional to 102.09 and 217.13 is: 461.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    102.09 : 217.13 = 217.13 : x
  2. Step 2: Convert to fraction form
    102.09/217.13 = 217.13/x
  3. Step 3: Cross multiply
    102.09x = 217.13 × 217.13
  4. Step 4: Simplify right side
    102.09x = 47,143.27
  5. Step 5: Solve for x
    x = 47,143.27/102.09
  6. Step 6: Final answer
    x = 461.76

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.