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Finding the Third Proportional to 117.69 and 257.69

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Solution

The third proportional to 117.69 and 257.69 is: 564.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    117.69 : 257.69 = 257.69 : x
  2. Step 2: Convert to fraction form
    117.69/257.69 = 257.69/x
  3. Step 3: Cross multiply
    117.69x = 257.69 × 257.69
  4. Step 4: Simplify right side
    117.69x = 66,402.85
  5. Step 5: Solve for x
    x = 66,402.85/117.69
  6. Step 6: Final answer
    x = 564.23

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.