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Finding the Third Proportional to 257.42 and 409.29

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Solution

The third proportional to 257.42 and 409.29 is: 650.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    257.42 : 409.29 = 409.29 : x
  2. Step 2: Convert to fraction form
    257.42/409.29 = 409.29/x
  3. Step 3: Cross multiply
    257.42x = 409.29 × 409.29
  4. Step 4: Simplify right side
    257.42x = 167,519.34
  5. Step 5: Solve for x
    x = 167,519.34/257.42
  6. Step 6: Final answer
    x = 650.77

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.