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Finding the Third Proportional to 205.66 and 289.20

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Solution

The third proportional to 205.66 and 289.20 is: 406.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.66 : 289.20 = 289.20 : x
  2. Step 2: Convert to fraction form
    205.66/289.20 = 289.20/x
  3. Step 3: Cross multiply
    205.66x = 289.20 × 289.20
  4. Step 4: Simplify right side
    205.66x = 83,633.93
  5. Step 5: Solve for x
    x = 83,633.93/205.66
  6. Step 6: Final answer
    x = 406.65

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.