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Finding the Third Proportional to 102.09 and 166.08

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Solution

The third proportional to 102.09 and 166.08 is: 270.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    102.09 : 166.08 = 166.08 : x
  2. Step 2: Convert to fraction form
    102.09/166.08 = 166.08/x
  3. Step 3: Cross multiply
    102.09x = 166.08 × 166.08
  4. Step 4: Simplify right side
    102.09x = 27,581.94
  5. Step 5: Solve for x
    x = 27,581.94/102.09
  6. Step 6: Final answer
    x = 270.16

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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.