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Finding the Third Proportional to 212 and 232.25

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Solution

The third proportional to 212 and 232.25 is: 254.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    212 : 232.25 = 232.25 : x
  2. Step 2: Convert to fraction form
    212/232.25 = 232.25/x
  3. Step 3: Cross multiply
    212x = 232.25 × 232.25
  4. Step 4: Simplify right side
    212x = 53,940.06
  5. Step 5: Solve for x
    x = 53,940.06/212
  6. Step 6: Final answer
    x = 254.43

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.