Finding the Third Proportional to 82.13 and 185.06

Step by Step Solution

1. Step 1: Write the proportion equation
   82.13 : 185.06 = 185.06 : x
2. Step 2: Convert to fraction form
   82.13/185.06 = 185.06/x
3. Step 3: Cross multiply
   82.13x = 185.06 × 185.06
4. Step 4: Simplify right side
   82.13x = 34,248.13
5. Step 5: Solve for x
   x = 34,248.13/82.13
6. Step 6: Final answer
   x = 417.02