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Finding the Third Proportional to 205.13 and 424.31

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Solution

The third proportional to 205.13 and 424.31 is: 877.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.13 : 424.31 = 424.31 : x
  2. Step 2: Convert to fraction form
    205.13/424.31 = 424.31/x
  3. Step 3: Cross multiply
    205.13x = 424.31 × 424.31
  4. Step 4: Simplify right side
    205.13x = 180,041.10
  5. Step 5: Solve for x
    x = 180,041.10/205.13
  6. Step 6: Final answer
    x = 877.71

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.