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Finding the Third Proportional to 196 and 213

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Solution

The third proportional to 196 and 213 is: 231.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    196 : 213 = 213 : x
  2. Step 2: Convert to fraction form
    196/213 = 213/x
  3. Step 3: Cross multiply
    196x = 213 × 213
  4. Step 4: Simplify right side
    196x = 45,369
  5. Step 5: Solve for x
    x = 45,369/196
  6. Step 6: Final answer
    x = 231.47

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.