Finding the Third Proportional to 406.69 and 565.31

Step by Step Solution

1. Step 1: Write the proportion equation
   406.69 : 565.31 = 565.31 : x
2. Step 2: Convert to fraction form
   406.69/565.31 = 565.31/x
3. Step 3: Cross multiply
   406.69x = 565.31 × 565.31
4. Step 4: Simplify right side
   406.69x = 319,578.22
5. Step 5: Solve for x
   x = 319,578.22/406.69
6. Step 6: Final answer
   x = 785.81