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Finding the Third Proportional to 1,056 and 1,729

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Solution

The third proportional to 1,056 and 1,729 is: 2,830.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,056 : 1,729 = 1,729 : x
  2. Step 2: Convert to fraction form
    1,056/1,729 = 1,729/x
  3. Step 3: Cross multiply
    1,056x = 1,729 × 1,729
  4. Step 4: Simplify right side
    1,056x = 2,989,441
  5. Step 5: Solve for x
    x = 2,989,441/1,056
  6. Step 6: Final answer
    x = 2,830.91

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Why These Related Problems?

These problems maintain the same ratio (1.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.