Finding the Third Proportional to 205.88 and 410.06

Step by Step Solution

1. Step 1: Write the proportion equation
   205.88 : 410.06 = 410.06 : x
2. Step 2: Convert to fraction form
   205.88/410.06 = 410.06/x
3. Step 3: Cross multiply
   205.88x = 410.06 × 410.06
4. Step 4: Simplify right side
   205.88x = 168,151.25
5. Step 5: Solve for x
   x = 168,151.25/205.88
6. Step 6: Final answer
   x = 816.76