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Finding the Third Proportional to 13,680 and 21,464

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Solution

The third proportional to 13,680 and 21,464 is: 33,677.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,680 : 21,464 = 21,464 : x
  2. Step 2: Convert to fraction form
    13,680/21,464 = 21,464/x
  3. Step 3: Cross multiply
    13,680x = 21,464 × 21,464
  4. Step 4: Simplify right side
    13,680x = 460,703,296
  5. Step 5: Solve for x
    x = 460,703,296/13,680
  6. Step 6: Final answer
    x = 33,677.14

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.