Finding the Third Proportional to 127.09 and 185.78

Step by Step Solution

1. Step 1: Write the proportion equation
   127.09 : 185.78 = 185.78 : x
2. Step 2: Convert to fraction form
   127.09/185.78 = 185.78/x
3. Step 3: Cross multiply
   127.09x = 185.78 × 185.78
4. Step 4: Simplify right side
   127.09x = 34,514.67
5. Step 5: Solve for x
   x = 34,514.67/127.09
6. Step 6: Final answer
   x = 271.57