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Finding the Third Proportional to 1,198 and 1,312

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Solution

The third proportional to 1,198 and 1,312 is: 1,436.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,198 : 1,312 = 1,312 : x
  2. Step 2: Convert to fraction form
    1,198/1,312 = 1,312/x
  3. Step 3: Cross multiply
    1,198x = 1,312 × 1,312
  4. Step 4: Simplify right side
    1,198x = 1,721,344
  5. Step 5: Solve for x
    x = 1,721,344/1,198
  6. Step 6: Final answer
    x = 1,436.85

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.