Finding the Third Proportional to 138.27 and 196.01

Step by Step Solution

1. Step 1: Write the proportion equation
   138.27 : 196.01 = 196.01 : x
2. Step 2: Convert to fraction form
   138.27/196.01 = 196.01/x
3. Step 3: Cross multiply
   138.27x = 196.01 × 196.01
4. Step 4: Simplify right side
   138.27x = 38,421.36
5. Step 5: Solve for x
   x = 38,421.36/138.27
6. Step 6: Final answer
   x = 277.87