Finding the Third Proportional to 382.54 and 825.82

Step by Step Solution

1. Step 1: Write the proportion equation
   382.54 : 825.82 = 825.82 : x
2. Step 2: Convert to fraction form
   382.54/825.82 = 825.82/x
3. Step 3: Cross multiply
   382.54x = 825.82 × 825.82
4. Step 4: Simplify right side
   382.54x = 681,979.19
5. Step 5: Solve for x
   x = 681,979.19/382.54
6. Step 6: Final answer
   x = 1,782.79