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Finding the Third Proportional to 5,416 and 7,071

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Solution

The third proportional to 5,416 and 7,071 is: 9,231.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,416 : 7,071 = 7,071 : x
  2. Step 2: Convert to fraction form
    5,416/7,071 = 7,071/x
  3. Step 3: Cross multiply
    5,416x = 7,071 × 7,071
  4. Step 4: Simplify right side
    5,416x = 49,999,041
  5. Step 5: Solve for x
    x = 49,999,041/5,416
  6. Step 6: Final answer
    x = 9,231.73

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.