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Finding the Third Proportional to 177.14 and 271.36

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Solution

The third proportional to 177.14 and 271.36 is: 415.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    177.14 : 271.36 = 271.36 : x
  2. Step 2: Convert to fraction form
    177.14/271.36 = 271.36/x
  3. Step 3: Cross multiply
    177.14x = 271.36 × 271.36
  4. Step 4: Simplify right side
    177.14x = 73,635.91
  5. Step 5: Solve for x
    x = 73,635.91/177.14
  6. Step 6: Final answer
    x = 415.69

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.