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Finding the Third Proportional to 102 and 216

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Solution

The third proportional to 102 and 216 is: 457.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    102 : 216 = 216 : x
  2. Step 2: Convert to fraction form
    102/216 = 216/x
  3. Step 3: Cross multiply
    102x = 216 × 216
  4. Step 4: Simplify right side
    102x = 46,656
  5. Step 5: Solve for x
    x = 46,656/102
  6. Step 6: Final answer
    x = 457.41

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.