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Finding the Third Proportional to 65 and 137

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Solution

The third proportional to 65 and 137 is: 288.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    65 : 137 = 137 : x
  2. Step 2: Convert to fraction form
    65/137 = 137/x
  3. Step 3: Cross multiply
    65x = 137 × 137
  4. Step 4: Simplify right side
    65x = 18,769
  5. Step 5: Solve for x
    x = 18,769/65
  6. Step 6: Final answer
    x = 288.75

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.