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Finding the Third Proportional to 205.45 and 414.91

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Solution

The third proportional to 205.45 and 414.91 is: 837.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.45 : 414.91 = 414.91 : x
  2. Step 2: Convert to fraction form
    205.45/414.91 = 414.91/x
  3. Step 3: Cross multiply
    205.45x = 414.91 × 414.91
  4. Step 4: Simplify right side
    205.45x = 172,153.68
  5. Step 5: Solve for x
    x = 172,153.68/205.45
  6. Step 6: Final answer
    x = 837.92

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.