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Finding the Third Proportional to 402 and 698.25

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Solution

The third proportional to 402 and 698.25 is: 1,212.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    402 : 698.25 = 698.25 : x
  2. Step 2: Convert to fraction form
    402/698.25 = 698.25/x
  3. Step 3: Cross multiply
    402x = 698.25 × 698.25
  4. Step 4: Simplify right side
    402x = 487,553.06
  5. Step 5: Solve for x
    x = 487,553.06/402
  6. Step 6: Final answer
    x = 1,212.82

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Why These Related Problems?

These problems maintain the same ratio (1.74) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.