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Finding the Third Proportional to 361 and 512

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Solution

The third proportional to 361 and 512 is: 726.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    361 : 512 = 512 : x
  2. Step 2: Convert to fraction form
    361/512 = 512/x
  3. Step 3: Cross multiply
    361x = 512 × 512
  4. Step 4: Simplify right side
    361x = 262,144
  5. Step 5: Solve for x
    x = 262,144/361
  6. Step 6: Final answer
    x = 726.16

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.