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Finding the Third Proportional to 456.19 and 614.81

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Solution

The third proportional to 456.19 and 614.81 is: 828.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    456.19 : 614.81 = 614.81 : x
  2. Step 2: Convert to fraction form
    456.19/614.81 = 614.81/x
  3. Step 3: Cross multiply
    456.19x = 614.81 × 614.81
  4. Step 4: Simplify right side
    456.19x = 377,994.41
  5. Step 5: Solve for x
    x = 377,994.41/456.19
  6. Step 6: Final answer
    x = 828.59

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.