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Finding the Third Proportional to 146.31 and 214.06

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Solution

The third proportional to 146.31 and 214.06 is: 313.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    146.31 : 214.06 = 214.06 : x
  2. Step 2: Convert to fraction form
    146.31/214.06 = 214.06/x
  3. Step 3: Cross multiply
    146.31x = 214.06 × 214.06
  4. Step 4: Simplify right side
    146.31x = 45,822.75
  5. Step 5: Solve for x
    x = 45,822.75/146.31
  6. Step 6: Final answer
    x = 313.18

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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.