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Finding the Third Proportional to 198 and 414

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Solution

The third proportional to 198 and 414 is: 865.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    198 : 414 = 414 : x
  2. Step 2: Convert to fraction form
    198/414 = 414/x
  3. Step 3: Cross multiply
    198x = 414 × 414
  4. Step 4: Simplify right side
    198x = 171,396
  5. Step 5: Solve for x
    x = 171,396/198
  6. Step 6: Final answer
    x = 865.64

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.