Finding the Third Proportional to 258.56 and 456.56

Step by Step Solution

1. Step 1: Write the proportion equation
   258.56 : 456.56 = 456.56 : x
2. Step 2: Convert to fraction form
   258.56/456.56 = 456.56/x
3. Step 3: Cross multiply
   258.56x = 456.56 × 456.56
4. Step 4: Simplify right side
   258.56x = 208,449.32
5. Step 5: Solve for x
   x = 208,449.32/258.56
6. Step 6: Final answer
   x = 806.19