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Finding the Third Proportional to 261.42 and 413.58

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Solution

The third proportional to 261.42 and 413.58 is: 654.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    261.42 : 413.58 = 413.58 : x
  2. Step 2: Convert to fraction form
    261.42/413.58 = 413.58/x
  3. Step 3: Cross multiply
    261.42x = 413.58 × 413.58
  4. Step 4: Simplify right side
    261.42x = 171,046.87
  5. Step 5: Solve for x
    x = 171,046.87/261.42
  6. Step 6: Final answer
    x = 654.29

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.