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Finding the Third Proportional to 196.65 and 414.65

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Solution

The third proportional to 196.65 and 414.65 is: 874.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    196.65 : 414.65 = 414.65 : x
  2. Step 2: Convert to fraction form
    196.65/414.65 = 414.65/x
  3. Step 3: Cross multiply
    196.65x = 414.65 × 414.65
  4. Step 4: Simplify right side
    196.65x = 171,934.95
  5. Step 5: Solve for x
    x = 171,934.95/196.65
  6. Step 6: Final answer
    x = 874.34

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.