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Finding the Third Proportional to 282.84 and 397.69

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Solution

The third proportional to 282.84 and 397.69 is: 559.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    282.84 : 397.69 = 397.69 : x
  2. Step 2: Convert to fraction form
    282.84/397.69 = 397.69/x
  3. Step 3: Cross multiply
    282.84x = 397.69 × 397.69
  4. Step 4: Simplify right side
    282.84x = 158,155.35
  5. Step 5: Solve for x
    x = 158,155.35/282.84
  6. Step 6: Final answer
    x = 559.16

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.