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Finding the Third Proportional to 138.66 and 197.09

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Solution

The third proportional to 138.66 and 197.09 is: 280.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    138.66 : 197.09 = 197.09 : x
  2. Step 2: Convert to fraction form
    138.66/197.09 = 197.09/x
  3. Step 3: Cross multiply
    138.66x = 197.09 × 197.09
  4. Step 4: Simplify right side
    138.66x = 38,842.87
  5. Step 5: Solve for x
    x = 38,842.87/138.66
  6. Step 6: Final answer
    x = 280.14

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.