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Finding the Third Proportional to 102 and 138

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Solution

The third proportional to 102 and 138 is: 186.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    102 : 138 = 138 : x
  2. Step 2: Convert to fraction form
    102/138 = 138/x
  3. Step 3: Cross multiply
    102x = 138 × 138
  4. Step 4: Simplify right side
    102x = 19,044
  5. Step 5: Solve for x
    x = 19,044/102
  6. Step 6: Final answer
    x = 186.71

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.