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Finding the Third Proportional to 542.81 and 686.06

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Solution

The third proportional to 542.81 and 686.06 is: 867.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    542.81 : 686.06 = 686.06 : x
  2. Step 2: Convert to fraction form
    542.81/686.06 = 686.06/x
  3. Step 3: Cross multiply
    542.81x = 686.06 × 686.06
  4. Step 4: Simplify right side
    542.81x = 470,681.75
  5. Step 5: Solve for x
    x = 470,681.75/542.81
  6. Step 6: Final answer
    x = 867.12

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Why These Related Problems?

These problems maintain the same ratio (1.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.