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Finding the Third Proportional to 106.59 and 165.09

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Solution

The third proportional to 106.59 and 165.09 is: 255.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    106.59 : 165.09 = 165.09 : x
  2. Step 2: Convert to fraction form
    106.59/165.09 = 165.09/x
  3. Step 3: Cross multiply
    106.59x = 165.09 × 165.09
  4. Step 4: Simplify right side
    106.59x = 27,255.95
  5. Step 5: Solve for x
    x = 27,255.95/106.59
  6. Step 6: Final answer
    x = 255.70

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.