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Finding the Third Proportional to 10,538 and 14,311

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Solution

The third proportional to 10,538 and 14,311 is: 19,434.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,538 : 14,311 = 14,311 : x
  2. Step 2: Convert to fraction form
    10,538/14,311 = 14,311/x
  3. Step 3: Cross multiply
    10,538x = 14,311 × 14,311
  4. Step 4: Simplify right side
    10,538x = 204,804,721
  5. Step 5: Solve for x
    x = 204,804,721/10,538
  6. Step 6: Final answer
    x = 19,434.88

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.