Finding the Third Proportional to 205.78 and 456.56

Step by Step Solution

1. Step 1: Write the proportion equation
   205.78 : 456.56 = 456.56 : x
2. Step 2: Convert to fraction form
   205.78/456.56 = 456.56/x
3. Step 3: Cross multiply
   205.78x = 456.56 × 456.56
4. Step 4: Simplify right side
   205.78x = 208,449.32
5. Step 5: Solve for x
   x = 208,449.32/205.78
6. Step 6: Final answer
   x = 1,012.97