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Finding the Third Proportional to 213 and 353

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Solution

The third proportional to 213 and 353 is: 585.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 353 = 353 : x
  2. Step 2: Convert to fraction form
    213/353 = 353/x
  3. Step 3: Cross multiply
    213x = 353 × 353
  4. Step 4: Simplify right side
    213x = 124,609
  5. Step 5: Solve for x
    x = 124,609/213
  6. Step 6: Final answer
    x = 585.02

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Why These Related Problems?

These problems maintain the same ratio (1.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.