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Finding the Third Proportional to 42 and 81

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Solution

The third proportional to 42 and 81 is: 156.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    42 : 81 = 81 : x
  2. Step 2: Convert to fraction form
    42/81 = 81/x
  3. Step 3: Cross multiply
    42x = 81 × 81
  4. Step 4: Simplify right side
    42x = 6,561
  5. Step 5: Solve for x
    x = 6,561/42
  6. Step 6: Final answer
    x = 156.21

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Why These Related Problems?

These problems maintain the same ratio (1.93) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.