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Finding the Third Proportional to 105.13 and 164.75

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Solution

The third proportional to 105.13 and 164.75 is: 258.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    105.13 : 164.75 = 164.75 : x
  2. Step 2: Convert to fraction form
    105.13/164.75 = 164.75/x
  3. Step 3: Cross multiply
    105.13x = 164.75 × 164.75
  4. Step 4: Simplify right side
    105.13x = 27,142.56
  5. Step 5: Solve for x
    x = 27,142.56/105.13
  6. Step 6: Final answer
    x = 258.19

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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.