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Finding the Third Proportional to 196.49 and 412.91

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Solution

The third proportional to 196.49 and 412.91 is: 867.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    196.49 : 412.91 = 412.91 : x
  2. Step 2: Convert to fraction form
    196.49/412.91 = 412.91/x
  3. Step 3: Cross multiply
    196.49x = 412.91 × 412.91
  4. Step 4: Simplify right side
    196.49x = 170,494.80
  5. Step 5: Solve for x
    x = 170,494.80/196.49
  6. Step 6: Final answer
    x = 867.71

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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.