Finding the Third Proportional to 82.59 and 178.41

Step by Step Solution

1. Step 1: Write the proportion equation
   82.59 : 178.41 = 178.41 : x
2. Step 2: Convert to fraction form
   82.59/178.41 = 178.41/x
3. Step 3: Cross multiply
   82.59x = 178.41 × 178.41
4. Step 4: Simplify right side
   82.59x = 31,828.79
5. Step 5: Solve for x
   x = 31,828.79/82.59
6. Step 6: Final answer
   x = 385.37