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Finding the Third Proportional to 209.81 and 289.13

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Solution

The third proportional to 209.81 and 289.13 is: 398.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.81 : 289.13 = 289.13 : x
  2. Step 2: Convert to fraction form
    209.81/289.13 = 289.13/x
  3. Step 3: Cross multiply
    209.81x = 289.13 × 289.13
  4. Step 4: Simplify right side
    209.81x = 83,593.27
  5. Step 5: Solve for x
    x = 83,593.27/209.81
  6. Step 6: Final answer
    x = 398.42

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.