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Finding the Third Proportional to 65 and 102.25

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Solution

The third proportional to 65 and 102.25 is: 160.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    65 : 102.25 = 102.25 : x
  2. Step 2: Convert to fraction form
    65/102.25 = 102.25/x
  3. Step 3: Cross multiply
    65x = 102.25 × 102.25
  4. Step 4: Simplify right side
    65x = 10,455.06
  5. Step 5: Solve for x
    x = 10,455.06/65
  6. Step 6: Final answer
    x = 160.85

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.