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Finding the Third Proportional to 8,096 and 14,336

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Solution

The third proportional to 8,096 and 14,336 is: 25,385.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,096 : 14,336 = 14,336 : x
  2. Step 2: Convert to fraction form
    8,096/14,336 = 14,336/x
  3. Step 3: Cross multiply
    8,096x = 14,336 × 14,336
  4. Step 4: Simplify right side
    8,096x = 205,520,896
  5. Step 5: Solve for x
    x = 205,520,896/8,096
  6. Step 6: Final answer
    x = 25,385.49

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.