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Finding the Fourth Proportional to 412.24, 564.56 and 406.84

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Solution

The fourth proportional to 412.24, 564.56 and 406.84 is: 557.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.24 : 564.56 = 406.84 : x
  2. Step 2: Convert to fraction form
    412.24/564.56 = 406.84/x
  3. Step 3: Cross multiply
    412.24x = 564.56 × 406.84
  4. Step 4: Simplify right side
    412.24x = 229,685.59
  5. Step 5: Solve for x
    x = 229,685.59/412.24
  6. Step 6: Final answer
    x = 557.16

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.