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Finding the Third Proportional to 289.88 and 414.09

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Solution

The third proportional to 289.88 and 414.09 is: 591.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    289.88 : 414.09 = 414.09 : x
  2. Step 2: Convert to fraction form
    289.88/414.09 = 414.09/x
  3. Step 3: Cross multiply
    289.88x = 414.09 × 414.09
  4. Step 4: Simplify right side
    289.88x = 171,473.63
  5. Step 5: Solve for x
    x = 171,473.63/289.88
  6. Step 6: Final answer
    x = 591.54

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.