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Finding the Third Proportional to 180.25 and 414.63

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Solution

The third proportional to 180.25 and 414.63 is: 953.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    180.25 : 414.63 = 414.63 : x
  2. Step 2: Convert to fraction form
    180.25/414.63 = 414.63/x
  3. Step 3: Cross multiply
    180.25x = 414.63 × 414.63
  4. Step 4: Simplify right side
    180.25x = 171,913.89
  5. Step 5: Solve for x
    x = 171,913.89/180.25
  6. Step 6: Final answer
    x = 953.75

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.