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Finding the Third Proportional to 102,144 and 216,816

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Solution

The third proportional to 102,144 and 216,816 is: 460,224.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,144 : 216,816 = 216,816 : x
  2. Step 2: Convert to fraction form
    102,144/216,816 = 216,816/x
  3. Step 3: Cross multiply
    102,144x = 216,816 × 216,816
  4. Step 4: Simplify right side
    102,144x = 47,009,177,856
  5. Step 5: Solve for x
    x = 47,009,177,856/102,144
  6. Step 6: Final answer
    x = 460,224.56

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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.