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Finding the Third Proportional to 259.13 and 416.81

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Solution

The third proportional to 259.13 and 416.81 is: 670.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    259.13 : 416.81 = 416.81 : x
  2. Step 2: Convert to fraction form
    259.13/416.81 = 416.81/x
  3. Step 3: Cross multiply
    259.13x = 416.81 × 416.81
  4. Step 4: Simplify right side
    259.13x = 173,732.66
  5. Step 5: Solve for x
    x = 173,732.66/259.13
  6. Step 6: Final answer
    x = 670.46

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.