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Finding the Third Proportional to 686.81 and 1,206.56

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Solution

The third proportional to 686.81 and 1,206.56 is: 2,119.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    686.81 : 1,206.56 = 1,206.56 : x
  2. Step 2: Convert to fraction form
    686.81/1,206.56 = 1,206.56/x
  3. Step 3: Cross multiply
    686.81x = 1,206.56 × 1,206.56
  4. Step 4: Simplify right side
    686.81x = 1,455,793.07
  5. Step 5: Solve for x
    x = 1,455,793.07/686.81
  6. Step 6: Final answer
    x = 2,119.64

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Why These Related Problems?

These problems maintain the same ratio (1.76) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.