Finding the Third Proportional to 120 and 185.38

Step by Step Solution

1. Step 1: Write the proportion equation
   120 : 185.38 = 185.38 : x
2. Step 2: Convert to fraction form
   120/185.38 = 185.38/x
3. Step 3: Cross multiply
   120x = 185.38 × 185.38
4. Step 4: Simplify right side
   120x = 34,363.89
5. Step 5: Solve for x
   x = 34,363.89/120
6. Step 6: Final answer
   x = 286.37