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Finding the Third Proportional to 102.75 and 214.06

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Solution

The third proportional to 102.75 and 214.06 is: 445.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    102.75 : 214.06 = 214.06 : x
  2. Step 2: Convert to fraction form
    102.75/214.06 = 214.06/x
  3. Step 3: Cross multiply
    102.75x = 214.06 × 214.06
  4. Step 4: Simplify right side
    102.75x = 45,822.75
  5. Step 5: Solve for x
    x = 45,822.75/102.75
  6. Step 6: Final answer
    x = 445.96

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.