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Finding the Third Proportional to 212.25 and 322.31

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Solution

The third proportional to 212.25 and 322.31 is: 489.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    212.25 : 322.31 = 322.31 : x
  2. Step 2: Convert to fraction form
    212.25/322.31 = 322.31/x
  3. Step 3: Cross multiply
    212.25x = 322.31 × 322.31
  4. Step 4: Simplify right side
    212.25x = 103,885.35
  5. Step 5: Solve for x
    x = 103,885.35/212.25
  6. Step 6: Final answer
    x = 489.45

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.