Finding the Third Proportional to 126 and 196.50

Step by Step Solution

1. Step 1: Write the proportion equation
   126 : 196.50 = 196.50 : x
2. Step 2: Convert to fraction form
   126/196.50 = 196.50/x
3. Step 3: Cross multiply
   126x = 196.50 × 196.50
4. Step 4: Simplify right side
   126x = 38,612.25
5. Step 5: Solve for x
   x = 38,612.25/126
6. Step 6: Final answer
   x = 306.45