Finding the Third Proportional to 105.06 and 164.56

Step by Step Solution

1. Step 1: Write the proportion equation
   105.06 : 164.56 = 164.56 : x
2. Step 2: Convert to fraction form
   105.06/164.56 = 164.56/x
3. Step 3: Cross multiply
   105.06x = 164.56 × 164.56
4. Step 4: Simplify right side
   105.06x = 27,080.82
5. Step 5: Solve for x
   x = 27,080.82/105.06
6. Step 6: Final answer
   x = 257.76