Finding the Third Proportional to 82.50 and 178.50

Step by Step Solution

1. Step 1: Write the proportion equation
   82.50 : 178.50 = 178.50 : x
2. Step 2: Convert to fraction form
   82.50/178.50 = 178.50/x
3. Step 3: Cross multiply
   82.50x = 178.50 × 178.50
4. Step 4: Simplify right side
   82.50x = 31,862.25
5. Step 5: Solve for x
   x = 31,862.25/82.50
6. Step 6: Final answer
   x = 386.21