Finding the Fourth Proportional to 498.01, 746.56 and 457.01

Step by Step Solution

1. Step 1: Write the proportion equation
   498.01 : 746.56 = 457.01 : x
2. Step 2: Convert to fraction form
   498.01/746.56 = 457.01/x
3. Step 3: Cross multiply
   498.01x = 746.56 × 457.01
4. Step 4: Simplify right side
   498.01x = 341,185.39
5. Step 5: Solve for x
   x = 341,185.39/498.01
6. Step 6: Final answer
   x = 685.10