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Finding the Third Proportional to 144 and 212.25

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Solution

The third proportional to 144 and 212.25 is: 312.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    144 : 212.25 = 212.25 : x
  2. Step 2: Convert to fraction form
    144/212.25 = 212.25/x
  3. Step 3: Cross multiply
    144x = 212.25 × 212.25
  4. Step 4: Simplify right side
    144x = 45,050.06
  5. Step 5: Solve for x
    x = 45,050.06/144
  6. Step 6: Final answer
    x = 312.85

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.