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Finding the Third Proportional to 1,728 and 3,412

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Solution

The third proportional to 1,728 and 3,412 is: 6,737.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,728 : 3,412 = 3,412 : x
  2. Step 2: Convert to fraction form
    1,728/3,412 = 3,412/x
  3. Step 3: Cross multiply
    1,728x = 3,412 × 3,412
  4. Step 4: Simplify right side
    1,728x = 11,641,744
  5. Step 5: Solve for x
    x = 11,641,744/1,728
  6. Step 6: Final answer
    x = 6,737.12

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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.