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Finding the Third Proportional to 456.84 and 689.34

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Solution

The third proportional to 456.84 and 689.34 is: 1,040.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    456.84 : 689.34 = 689.34 : x
  2. Step 2: Convert to fraction form
    456.84/689.34 = 689.34/x
  3. Step 3: Cross multiply
    456.84x = 689.34 × 689.34
  4. Step 4: Simplify right side
    456.84x = 475,194.81
  5. Step 5: Solve for x
    x = 475,194.81/456.84
  6. Step 6: Final answer
    x = 1,040.18

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.