Finding the Third Proportional to 258.56 and 412.78

Step by Step Solution

1. Step 1: Write the proportion equation
   258.56 : 412.78 = 412.78 : x
2. Step 2: Convert to fraction form
   258.56/412.78 = 412.78/x
3. Step 3: Cross multiply
   258.56x = 412.78 × 412.78
4. Step 4: Simplify right side
   258.56x = 170,388.36
5. Step 5: Solve for x
   x = 170,388.36/258.56
6. Step 6: Final answer
   x = 658.98