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Finding the Third Proportional to 414.88 and 586.69

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Solution

The third proportional to 414.88 and 586.69 is: 829.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.88 : 586.69 = 586.69 : x
  2. Step 2: Convert to fraction form
    414.88/586.69 = 586.69/x
  3. Step 3: Cross multiply
    414.88x = 586.69 × 586.69
  4. Step 4: Simplify right side
    414.88x = 344,202.22
  5. Step 5: Solve for x
    x = 344,202.22/414.88
  6. Step 6: Final answer
    x = 829.65

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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.