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Finding the Third Proportional to 289.69 and 408.09

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Solution

The third proportional to 289.69 and 408.09 is: 574.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    289.69 : 408.09 = 408.09 : x
  2. Step 2: Convert to fraction form
    289.69/408.09 = 408.09/x
  3. Step 3: Cross multiply
    289.69x = 408.09 × 408.09
  4. Step 4: Simplify right side
    289.69x = 166,540.51
  5. Step 5: Solve for x
    x = 166,540.51/289.69
  6. Step 6: Final answer
    x = 574.90

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.