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Finding the Third Proportional to 180,144 and 270,216

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Solution

The third proportional to 180,144 and 270,216 is: 405,324

Step by Step Solution

  1. Step 1: Write the proportion equation
    180,144 : 270,216 = 270,216 : x
  2. Step 2: Convert to fraction form
    180,144/270,216 = 270,216/x
  3. Step 3: Cross multiply
    180,144x = 270,216 × 270,216
  4. Step 4: Simplify right side
    180,144x = 73,016,686,656
  5. Step 5: Solve for x
    x = 73,016,686,656/180,144
  6. Step 6: Final answer
    x = 405,324

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.