Finding the Third Proportional to 105.06 and 165.94

Step by Step Solution

1. Step 1: Write the proportion equation
   105.06 : 165.94 = 165.94 : x
2. Step 2: Convert to fraction form
   105.06/165.94 = 165.94/x
3. Step 3: Cross multiply
   105.06x = 165.94 × 165.94
4. Step 4: Simplify right side
   105.06x = 27,535.25
5. Step 5: Solve for x
   x = 27,535.25/105.06
6. Step 6: Final answer
   x = 262.08