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Finding the Third Proportional to 212.75 and 282.25

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Solution

The third proportional to 212.75 and 282.25 is: 374.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    212.75 : 282.25 = 282.25 : x
  2. Step 2: Convert to fraction form
    212.75/282.25 = 282.25/x
  3. Step 3: Cross multiply
    212.75x = 282.25 × 282.25
  4. Step 4: Simplify right side
    212.75x = 79,665.06
  5. Step 5: Solve for x
    x = 79,665.06/212.75
  6. Step 6: Final answer
    x = 374.45

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.