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Finding the Third Proportional to 680 and 1,414

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Solution

The third proportional to 680 and 1,414 is: 2,940.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    680 : 1,414 = 1,414 : x
  2. Step 2: Convert to fraction form
    680/1,414 = 1,414/x
  3. Step 3: Cross multiply
    680x = 1,414 × 1,414
  4. Step 4: Simplify right side
    680x = 1,999,396
  5. Step 5: Solve for x
    x = 1,999,396/680
  6. Step 6: Final answer
    x = 2,940.29

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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.