Finding the Third Proportional to 105.75 and 164.53

Step by Step Solution

1. Step 1: Write the proportion equation
   105.75 : 164.53 = 164.53 : x
2. Step 2: Convert to fraction form
   105.75/164.53 = 164.53/x
3. Step 3: Cross multiply
   105.75x = 164.53 × 164.53
4. Step 4: Simplify right side
   105.75x = 27,070.53
5. Step 5: Solve for x
   x = 27,070.53/105.75
6. Step 6: Final answer
   x = 255.99