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Finding the Third Proportional to 289 and 462.25

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Solution

The third proportional to 289 and 462.25 is: 739.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    289 : 462.25 = 462.25 : x
  2. Step 2: Convert to fraction form
    289/462.25 = 462.25/x
  3. Step 3: Cross multiply
    289x = 462.25 × 462.25
  4. Step 4: Simplify right side
    289x = 213,675.06
  5. Step 5: Solve for x
    x = 213,675.06/289
  6. Step 6: Final answer
    x = 739.36

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.