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Finding the Third Proportional to 192.25 and 282.25

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Solution

The third proportional to 192.25 and 282.25 is: 414.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    192.25 : 282.25 = 282.25 : x
  2. Step 2: Convert to fraction form
    192.25/282.25 = 282.25/x
  3. Step 3: Cross multiply
    192.25x = 282.25 × 282.25
  4. Step 4: Simplify right side
    192.25x = 79,665.06
  5. Step 5: Solve for x
    x = 79,665.06/192.25
  6. Step 6: Final answer
    x = 414.38

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.