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Finding the Third Proportional to 65 and 106

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Solution

The third proportional to 65 and 106 is: 172.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    65 : 106 = 106 : x
  2. Step 2: Convert to fraction form
    65/106 = 106/x
  3. Step 3: Cross multiply
    65x = 106 × 106
  4. Step 4: Simplify right side
    65x = 11,236
  5. Step 5: Solve for x
    x = 11,236/65
  6. Step 6: Final answer
    x = 172.86

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.