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Finding the Third Proportional to 256 and 397

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Solution

The third proportional to 256 and 397 is: 615.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    256 : 397 = 397 : x
  2. Step 2: Convert to fraction form
    256/397 = 397/x
  3. Step 3: Cross multiply
    256x = 397 × 397
  4. Step 4: Simplify right side
    256x = 157,609
  5. Step 5: Solve for x
    x = 157,609/256
  6. Step 6: Final answer
    x = 615.66

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These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.