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Finding the Third Proportional to 312.25 and 456.38

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Solution

The third proportional to 312.25 and 456.38 is: 667.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    312.25 : 456.38 = 456.38 : x
  2. Step 2: Convert to fraction form
    312.25/456.38 = 456.38/x
  3. Step 3: Cross multiply
    312.25x = 456.38 × 456.38
  4. Step 4: Simplify right side
    312.25x = 208,278.14
  5. Step 5: Solve for x
    x = 208,278.14/312.25
  6. Step 6: Final answer
    x = 667.02

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.