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Finding the Third Proportional to 81 and 144

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Solution

The third proportional to 81 and 144 is: 256

Step by Step Solution

  1. Step 1: Write the proportion equation
    81 : 144 = 144 : x
  2. Step 2: Convert to fraction form
    81/144 = 144/x
  3. Step 3: Cross multiply
    81x = 144 × 144
  4. Step 4: Simplify right side
    81x = 20,736
  5. Step 5: Solve for x
    x = 20,736/81
  6. Step 6: Final answer
    x = 256

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Why These Related Problems?

These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.