Finding the Third Proportional to 256 and 577.38

Step by Step Solution

1. Step 1: Write the proportion equation
   256 : 577.38 = 577.38 : x
2. Step 2: Convert to fraction form
   256/577.38 = 577.38/x
3. Step 3: Cross multiply
   256x = 577.38 × 577.38
4. Step 4: Simplify right side
   256x = 333,361.89
5. Step 5: Solve for x
   x = 333,361.89/256
6. Step 6: Final answer
   x = 1,302.19