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Finding the Third Proportional to 565 and 1,213

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Solution

The third proportional to 565 and 1,213 is: 2,604.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    565 : 1,213 = 1,213 : x
  2. Step 2: Convert to fraction form
    565/1,213 = 1,213/x
  3. Step 3: Cross multiply
    565x = 1,213 × 1,213
  4. Step 4: Simplify right side
    565x = 1,471,369
  5. Step 5: Solve for x
    x = 1,471,369/565
  6. Step 6: Final answer
    x = 2,604.19

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.