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Finding the Third Proportional to 421.14 and 534.09

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Solution

The third proportional to 421.14 and 534.09 is: 677.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    421.14 : 534.09 = 534.09 : x
  2. Step 2: Convert to fraction form
    421.14/534.09 = 534.09/x
  3. Step 3: Cross multiply
    421.14x = 534.09 × 534.09
  4. Step 4: Simplify right side
    421.14x = 285,256.13
  5. Step 5: Solve for x
    x = 285,256.13/421.14
  6. Step 6: Final answer
    x = 677.35

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.