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Finding the Third Proportional to 120 and 223

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Solution

The third proportional to 120 and 223 is: 414.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    120 : 223 = 223 : x
  2. Step 2: Convert to fraction form
    120/223 = 223/x
  3. Step 3: Cross multiply
    120x = 223 × 223
  4. Step 4: Simplify right side
    120x = 49,729
  5. Step 5: Solve for x
    x = 49,729/120
  6. Step 6: Final answer
    x = 414.41

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.