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Finding the Third Proportional to 81,972 and 180,021

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Solution

The third proportional to 81,972 and 180,021 is: 395,349.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,972 : 180,021 = 180,021 : x
  2. Step 2: Convert to fraction form
    81,972/180,021 = 180,021/x
  3. Step 3: Cross multiply
    81,972x = 180,021 × 180,021
  4. Step 4: Simplify right side
    81,972x = 32,407,560,441
  5. Step 5: Solve for x
    x = 32,407,560,441/81,972
  6. Step 6: Final answer
    x = 395,349.15

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.