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Finding the Third Proportional to 31.44 and 82.06

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Solution

The third proportional to 31.44 and 82.06 is: 214.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    31.44 : 82.06 = 82.06 : x
  2. Step 2: Convert to fraction form
    31.44/82.06 = 82.06/x
  3. Step 3: Cross multiply
    31.44x = 82.06 × 82.06
  4. Step 4: Simplify right side
    31.44x = 6,734.25
  5. Step 5: Solve for x
    x = 6,734.25/31.44
  6. Step 6: Final answer
    x = 214.21

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Why These Related Problems?

These problems maintain the same ratio (2.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.