Finding the Third Proportional to 82,144 and 177,392

Step by Step Solution

1. Step 1: Write the proportion equation
   82,144 : 177,392 = 177,392 : x
2. Step 2: Convert to fraction form
   82,144/177,392 = 177,392/x
3. Step 3: Cross multiply
   82,144x = 177,392 × 177,392
4. Step 4: Simplify right side
   82,144x = 31,467,921,664
5. Step 5: Solve for x
   x = 31,467,921,664/82,144
6. Step 6: Final answer
   x = 383,082.41