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Finding the Third Proportional to 256 and 289

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Solution

The third proportional to 256 and 289 is: 326.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    256 : 289 = 289 : x
  2. Step 2: Convert to fraction form
    256/289 = 289/x
  3. Step 3: Cross multiply
    256x = 289 × 289
  4. Step 4: Simplify right side
    256x = 83,521
  5. Step 5: Solve for x
    x = 83,521/256
  6. Step 6: Final answer
    x = 326.25

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.