Finding the Third Proportional to 82.69 and 177.94

Step by Step Solution

1. Step 1: Write the proportion equation
   82.69 : 177.94 = 177.94 : x
2. Step 2: Convert to fraction form
   82.69/177.94 = 177.94/x
3. Step 3: Cross multiply
   82.69x = 177.94 × 177.94
4. Step 4: Simplify right side
   82.69x = 31,661.75
5. Step 5: Solve for x
   x = 31,661.75/82.69
6. Step 6: Final answer
   x = 382.91