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Finding the Third Proportional to 1,414 and 2,986

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Solution

The third proportional to 1,414 and 2,986 is: 6,305.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,414 : 2,986 = 2,986 : x
  2. Step 2: Convert to fraction form
    1,414/2,986 = 2,986/x
  3. Step 3: Cross multiply
    1,414x = 2,986 × 2,986
  4. Step 4: Simplify right side
    1,414x = 8,916,196
  5. Step 5: Solve for x
    x = 8,916,196/1,414
  6. Step 6: Final answer
    x = 6,305.65

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.