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Finding the Third Proportional to 290.51 and 414.12

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Solution

The third proportional to 290.51 and 414.12 is: 590.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    290.51 : 414.12 = 414.12 : x
  2. Step 2: Convert to fraction form
    290.51/414.12 = 414.12/x
  3. Step 3: Cross multiply
    290.51x = 414.12 × 414.12
  4. Step 4: Simplify right side
    290.51x = 171,497.90
  5. Step 5: Solve for x
    x = 171,497.90/290.51
  6. Step 6: Final answer
    x = 590.33

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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.