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Finding the Third Proportional to 135.74 and 209.46

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Solution

The third proportional to 135.74 and 209.46 is: 323.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    135.74 : 209.46 = 209.46 : x
  2. Step 2: Convert to fraction form
    135.74/209.46 = 209.46/x
  3. Step 3: Cross multiply
    135.74x = 209.46 × 209.46
  4. Step 4: Simplify right side
    135.74x = 43,873.88
  5. Step 5: Solve for x
    x = 43,873.88/135.74
  6. Step 6: Final answer
    x = 323.22

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.