Finding the Third Proportional to 456.75 and 684.56

Step by Step Solution

1. Step 1: Write the proportion equation
   456.75 : 684.56 = 684.56 : x
2. Step 2: Convert to fraction form
   456.75/684.56 = 684.56/x
3. Step 3: Cross multiply
   456.75x = 684.56 × 684.56
4. Step 4: Simplify right side
   456.75x = 468,625.82
5. Step 5: Solve for x
   x = 468,625.82/456.75
6. Step 6: Final answer
   x = 1,026.00