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Finding the Third Proportional to 206.75 and 421.38

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Solution

The third proportional to 206.75 and 421.38 is: 858.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    206.75 : 421.38 = 421.38 : x
  2. Step 2: Convert to fraction form
    206.75/421.38 = 421.38/x
  3. Step 3: Cross multiply
    206.75x = 421.38 × 421.38
  4. Step 4: Simplify right side
    206.75x = 177,556.89
  5. Step 5: Solve for x
    x = 177,556.89/206.75
  6. Step 6: Final answer
    x = 858.80

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.