Finding the Third Proportional to 274.78 and 414.89

Step by Step Solution

1. Step 1: Write the proportion equation
   274.78 : 414.89 = 414.89 : x
2. Step 2: Convert to fraction form
   274.78/414.89 = 414.89/x
3. Step 3: Cross multiply
   274.78x = 414.89 × 414.89
4. Step 4: Simplify right side
   274.78x = 172,134.23
5. Step 5: Solve for x
   x = 172,134.23/274.78
6. Step 6: Final answer
   x = 626.44