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Finding the Third Proportional to 200.05 and 414.57

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Solution

The third proportional to 200.05 and 414.57 is: 859.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    200.05 : 414.57 = 414.57 : x
  2. Step 2: Convert to fraction form
    200.05/414.57 = 414.57/x
  3. Step 3: Cross multiply
    200.05x = 414.57 × 414.57
  4. Step 4: Simplify right side
    200.05x = 171,869.35
  5. Step 5: Solve for x
    x = 171,869.35/200.05
  6. Step 6: Final answer
    x = 859.14

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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.