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Finding the Third Proportional to 198.47 and 413.06

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Solution

The third proportional to 198.47 and 413.06 is: 859.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    198.47 : 413.06 = 413.06 : x
  2. Step 2: Convert to fraction form
    198.47/413.06 = 413.06/x
  3. Step 3: Cross multiply
    198.47x = 413.06 × 413.06
  4. Step 4: Simplify right side
    198.47x = 170,620.63
  5. Step 5: Solve for x
    x = 170,620.63/198.47
  6. Step 6: Final answer
    x = 859.69

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.