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Finding the Third Proportional to 919 and 1,412

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Solution

The third proportional to 919 and 1,412 is: 2,169.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    919 : 1,412 = 1,412 : x
  2. Step 2: Convert to fraction form
    919/1,412 = 1,412/x
  3. Step 3: Cross multiply
    919x = 1,412 × 1,412
  4. Step 4: Simplify right side
    919x = 1,993,744
  5. Step 5: Solve for x
    x = 1,993,744/919
  6. Step 6: Final answer
    x = 2,169.47

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.