Finding the Third Proportional to 82.50 and 120.09

Step by Step Solution

1. Step 1: Write the proportion equation
   82.50 : 120.09 = 120.09 : x
2. Step 2: Convert to fraction form
   82.50/120.09 = 120.09/x
3. Step 3: Cross multiply
   82.50x = 120.09 × 120.09
4. Step 4: Simplify right side
   82.50x = 14,422.51
5. Step 5: Solve for x
   x = 14,422.51/82.50
6. Step 6: Final answer
   x = 174.82