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Finding the Third Proportional to 1,414 and 2,105

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Solution

The third proportional to 1,414 and 2,105 is: 3,133.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,414 : 2,105 = 2,105 : x
  2. Step 2: Convert to fraction form
    1,414/2,105 = 2,105/x
  3. Step 3: Cross multiply
    1,414x = 2,105 × 2,105
  4. Step 4: Simplify right side
    1,414x = 4,431,025
  5. Step 5: Solve for x
    x = 4,431,025/1,414
  6. Step 6: Final answer
    x = 3,133.68

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.