Finding the Third Proportional to 102.38 and 199.59

Step by Step Solution

1. Step 1: Write the proportion equation
   102.38 : 199.59 = 199.59 : x
2. Step 2: Convert to fraction form
   102.38/199.59 = 199.59/x
3. Step 3: Cross multiply
   102.38x = 199.59 × 199.59
4. Step 4: Simplify right side
   102.38x = 39,837.67
5. Step 5: Solve for x
   x = 39,837.67/102.38
6. Step 6: Final answer
   x = 389.13