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Finding the Third Proportional to 212.25 and 285.75

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Solution

The third proportional to 212.25 and 285.75 is: 384.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    212.25 : 285.75 = 285.75 : x
  2. Step 2: Convert to fraction form
    212.25/285.75 = 285.75/x
  3. Step 3: Cross multiply
    212.25x = 285.75 × 285.75
  4. Step 4: Simplify right side
    212.25x = 81,653.06
  5. Step 5: Solve for x
    x = 81,653.06/212.25
  6. Step 6: Final answer
    x = 384.70

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.