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Finding the Third Proportional to 252.88 and 414.13

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Solution

The third proportional to 252.88 and 414.13 is: 678.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    252.88 : 414.13 = 414.13 : x
  2. Step 2: Convert to fraction form
    252.88/414.13 = 414.13/x
  3. Step 3: Cross multiply
    252.88x = 414.13 × 414.13
  4. Step 4: Simplify right side
    252.88x = 171,499.52
  5. Step 5: Solve for x
    x = 171,499.52/252.88
  6. Step 6: Final answer
    x = 678.20

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Why These Related Problems?

These problems maintain the same ratio (1.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.