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Finding the Third Proportional to 1,684 and 2,712

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Solution

The third proportional to 1,684 and 2,712 is: 4,367.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,684 : 2,712 = 2,712 : x
  2. Step 2: Convert to fraction form
    1,684/2,712 = 2,712/x
  3. Step 3: Cross multiply
    1,684x = 2,712 × 2,712
  4. Step 4: Simplify right side
    1,684x = 7,354,944
  5. Step 5: Solve for x
    x = 7,354,944/1,684
  6. Step 6: Final answer
    x = 4,367.54

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.