Finding the Third Proportional to 413.16 and 562.78

Step by Step Solution

1. Step 1: Write the proportion equation
   413.16 : 562.78 = 562.78 : x
2. Step 2: Convert to fraction form
   413.16/562.78 = 562.78/x
3. Step 3: Cross multiply
   413.16x = 562.78 × 562.78
4. Step 4: Simplify right side
   413.16x = 316,722.74
5. Step 5: Solve for x
   x = 316,722.74/413.16
6. Step 6: Final answer
   x = 766.59