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Finding the Third Proportional to 105 and 213

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Solution

The third proportional to 105 and 213 is: 432.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    105 : 213 = 213 : x
  2. Step 2: Convert to fraction form
    105/213 = 213/x
  3. Step 3: Cross multiply
    105x = 213 × 213
  4. Step 4: Simplify right side
    105x = 45,369
  5. Step 5: Solve for x
    x = 45,369/105
  6. Step 6: Final answer
    x = 432.09

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.