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Finding the Fourth Proportional to 413.24, 565.93 and 407.84

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Solution

The fourth proportional to 413.24, 565.93 and 407.84 is: 558.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    413.24 : 565.93 = 407.84 : x
  2. Step 2: Convert to fraction form
    413.24/565.93 = 407.84/x
  3. Step 3: Cross multiply
    413.24x = 565.93 × 407.84
  4. Step 4: Simplify right side
    413.24x = 230,808.89
  5. Step 5: Solve for x
    x = 230,808.89/413.24
  6. Step 6: Final answer
    x = 558.53

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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.