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Finding the Third Proportional to 408.16 and 565.73

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Solution

The third proportional to 408.16 and 565.73 is: 784.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    408.16 : 565.73 = 565.73 : x
  2. Step 2: Convert to fraction form
    408.16/565.73 = 565.73/x
  3. Step 3: Cross multiply
    408.16x = 565.73 × 565.73
  4. Step 4: Simplify right side
    408.16x = 320,055.38
  5. Step 5: Solve for x
    x = 320,055.38/408.16
  6. Step 6: Final answer
    x = 784.13

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Why These Related Problems?

These problems maintain the same ratio (1.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.