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Finding the Third Proportional to 7,071 and 13,965

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Solution

The third proportional to 7,071 and 13,965 is: 27,580.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,071 : 13,965 = 13,965 : x
  2. Step 2: Convert to fraction form
    7,071/13,965 = 13,965/x
  3. Step 3: Cross multiply
    7,071x = 13,965 × 13,965
  4. Step 4: Simplify right side
    7,071x = 195,021,225
  5. Step 5: Solve for x
    x = 195,021,225/7,071
  6. Step 6: Final answer
    x = 27,580.43

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Why These Related Problems?

These problems maintain the same ratio (1.97) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.