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Finding the Third Proportional to 286.13 and 413.44

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Solution

The third proportional to 286.13 and 413.44 is: 597.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    286.13 : 413.44 = 413.44 : x
  2. Step 2: Convert to fraction form
    286.13/413.44 = 413.44/x
  3. Step 3: Cross multiply
    286.13x = 413.44 × 413.44
  4. Step 4: Simplify right side
    286.13x = 170,930.57
  5. Step 5: Solve for x
    x = 170,930.57/286.13
  6. Step 6: Final answer
    x = 597.40

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.