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Finding the Third Proportional to 1,414 and 3,514

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Solution

The third proportional to 1,414 and 3,514 is: 8,732.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,414 : 3,514 = 3,514 : x
  2. Step 2: Convert to fraction form
    1,414/3,514 = 3,514/x
  3. Step 3: Cross multiply
    1,414x = 3,514 × 3,514
  4. Step 4: Simplify right side
    1,414x = 12,348,196
  5. Step 5: Solve for x
    x = 12,348,196/1,414
  6. Step 6: Final answer
    x = 8,732.81

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Why These Related Problems?

These problems maintain the same ratio (2.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.