Finding the Third Proportional to 146.80 and 205.23

Step by Step Solution

1. Step 1: Write the proportion equation
   146.80 : 205.23 = 205.23 : x
2. Step 2: Convert to fraction form
   146.80/205.23 = 205.23/x
3. Step 3: Cross multiply
   146.80x = 205.23 × 205.23
4. Step 4: Simplify right side
   146.80x = 42,121.15
5. Step 5: Solve for x
   x = 42,121.15/146.80
6. Step 6: Final answer
   x = 286.93