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Finding the Third Proportional to 314.19 and 413.13

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Solution

The third proportional to 314.19 and 413.13 is: 543.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    314.19 : 413.13 = 413.13 : x
  2. Step 2: Convert to fraction form
    314.19/413.13 = 413.13/x
  3. Step 3: Cross multiply
    314.19x = 413.13 × 413.13
  4. Step 4: Simplify right side
    314.19x = 170,672.27
  5. Step 5: Solve for x
    x = 170,672.27/314.19
  6. Step 6: Final answer
    x = 543.22

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.