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Finding the Third Proportional to 406 and 578

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Solution

The third proportional to 406 and 578 is: 822.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    406 : 578 = 578 : x
  2. Step 2: Convert to fraction form
    406/578 = 578/x
  3. Step 3: Cross multiply
    406x = 578 × 578
  4. Step 4: Simplify right side
    406x = 334,084
  5. Step 5: Solve for x
    x = 334,084/406
  6. Step 6: Final answer
    x = 822.87

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These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.