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Finding the Third Proportional to 138.19 and 209.16

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Solution

The third proportional to 138.19 and 209.16 is: 316.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    138.19 : 209.16 = 209.16 : x
  2. Step 2: Convert to fraction form
    138.19/209.16 = 209.16/x
  3. Step 3: Cross multiply
    138.19x = 209.16 × 209.16
  4. Step 4: Simplify right side
    138.19x = 43,746.34
  5. Step 5: Solve for x
    x = 43,746.34/138.19
  6. Step 6: Final answer
    x = 316.57

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.