Finding the Third Proportional to 456.75 and 685.38

Step by Step Solution

1. Step 1: Write the proportion equation
   456.75 : 685.38 = 685.38 : x
2. Step 2: Convert to fraction form
   456.75/685.38 = 685.38/x
3. Step 3: Cross multiply
   456.75x = 685.38 × 685.38
4. Step 4: Simplify right side
   456.75x = 469,738.89
5. Step 5: Solve for x
   x = 469,738.89/456.75
6. Step 6: Final answer
   x = 1,028.44