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Finding the Third Proportional to 196.41 and 409.11

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Solution

The third proportional to 196.41 and 409.11 is: 852.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    196.41 : 409.11 = 409.11 : x
  2. Step 2: Convert to fraction form
    196.41/409.11 = 409.11/x
  3. Step 3: Cross multiply
    196.41x = 409.11 × 409.11
  4. Step 4: Simplify right side
    196.41x = 167,373.68
  5. Step 5: Solve for x
    x = 167,373.68/196.41
  6. Step 6: Final answer
    x = 852.17

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.