Finding the Third Proportional to 121.78 and 256.78

Step by Step Solution

1. Step 1: Write the proportion equation
   121.78 : 256.78 = 256.78 : x
2. Step 2: Convert to fraction form
   121.78/256.78 = 256.78/x
3. Step 3: Cross multiply
   121.78x = 256.78 × 256.78
4. Step 4: Simplify right side
   121.78x = 65,936.61
5. Step 5: Solve for x
   x = 65,936.61/121.78
6. Step 6: Final answer
   x = 541.43