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Finding the Third Proportional to 213.19 and 289.31

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Solution

The third proportional to 213.19 and 289.31 is: 392.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    213.19 : 289.31 = 289.31 : x
  2. Step 2: Convert to fraction form
    213.19/289.31 = 289.31/x
  3. Step 3: Cross multiply
    213.19x = 289.31 × 289.31
  4. Step 4: Simplify right side
    213.19x = 83,701.72
  5. Step 5: Solve for x
    x = 83,701.72/213.19
  6. Step 6: Final answer
    x = 392.62

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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.