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Finding the Third Proportional to 232.78 and 413.39

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Solution

The third proportional to 232.78 and 413.39 is: 734.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    232.78 : 413.39 = 413.39 : x
  2. Step 2: Convert to fraction form
    232.78/413.39 = 413.39/x
  3. Step 3: Cross multiply
    232.78x = 413.39 × 413.39
  4. Step 4: Simplify right side
    232.78x = 170,891.81
  5. Step 5: Solve for x
    x = 170,891.81/232.78
  6. Step 6: Final answer
    x = 734.13

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Why These Related Problems?

These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.