Finding the Third Proportional to 458.91 and 709.78

Step by Step Solution

1. Step 1: Write the proportion equation
   458.91 : 709.78 = 709.78 : x
2. Step 2: Convert to fraction form
   458.91/709.78 = 709.78/x
3. Step 3: Cross multiply
   458.91x = 709.78 × 709.78
4. Step 4: Simplify right side
   458.91x = 503,789.42
5. Step 5: Solve for x
   x = 503,789.42/458.91
6. Step 6: Final answer
   x = 1,097.80