Finding the Third Proportional to 116,138 and 177,538

Step by Step Solution

1. Step 1: Write the proportion equation
   116,138 : 177,538 = 177,538 : x
2. Step 2: Convert to fraction form
   116,138/177,538 = 177,538/x
3. Step 3: Cross multiply
   116,138x = 177,538 × 177,538
4. Step 4: Simplify right side
   116,138x = 31,519,741,444
5. Step 5: Solve for x
   x = 31,519,741,444/116,138
6. Step 6: Final answer
   x = 271,399.04