Finding the Third Proportional to 82.50 and 180.38

Step by Step Solution

1. Step 1: Write the proportion equation
   82.50 : 180.38 = 180.38 : x
2. Step 2: Convert to fraction form
   82.50/180.38 = 180.38/x
3. Step 3: Cross multiply
   82.50x = 180.38 × 180.38
4. Step 4: Simplify right side
   82.50x = 32,535.14
5. Step 5: Solve for x
   x = 32,535.14/82.50
6. Step 6: Final answer
   x = 394.37