Finding the Third Proportional to 516.38 and 781.31

Step by Step Solution

1. Step 1: Write the proportion equation
   516.38 : 781.31 = 781.31 : x
2. Step 2: Convert to fraction form
   516.38/781.31 = 781.31/x
3. Step 3: Cross multiply
   516.38x = 781.31 × 781.31
4. Step 4: Simplify right side
   516.38x = 610,449.22
5. Step 5: Solve for x
   x = 610,449.22/516.38
6. Step 6: Final answer
   x = 1,182.18