Finding the Third Proportional to 82.27 and 177.61

Step by Step Solution

1. Step 1: Write the proportion equation
   82.27 : 177.61 = 177.61 : x
2. Step 2: Convert to fraction form
   82.27/177.61 = 177.61/x
3. Step 3: Cross multiply
   82.27x = 177.61 × 177.61
4. Step 4: Simplify right side
   82.27x = 31,545.09
5. Step 5: Solve for x
   x = 31,545.09/82.27
6. Step 6: Final answer
   x = 383.45