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Finding the Third Proportional to 197.02 and 414.14

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Solution

The third proportional to 197.02 and 414.14 is: 870.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    197.02 : 414.14 = 414.14 : x
  2. Step 2: Convert to fraction form
    197.02/414.14 = 414.14/x
  3. Step 3: Cross multiply
    197.02x = 414.14 × 414.14
  4. Step 4: Simplify right side
    197.02x = 171,512.46
  5. Step 5: Solve for x
    x = 171,512.46/197.02
  6. Step 6: Final answer
    x = 870.55

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.