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Finding the Third Proportional to 106 and 180

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Solution

The third proportional to 106 and 180 is: 305.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    106 : 180 = 180 : x
  2. Step 2: Convert to fraction form
    106/180 = 180/x
  3. Step 3: Cross multiply
    106x = 180 × 180
  4. Step 4: Simplify right side
    106x = 32,400
  5. Step 5: Solve for x
    x = 32,400/106
  6. Step 6: Final answer
    x = 305.66

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Why These Related Problems?

These problems maintain the same ratio (1.70) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.