Finding the Third Proportional to 512.69 and 681.38

Step by Step Solution

1. Step 1: Write the proportion equation
   512.69 : 681.38 = 681.38 : x
2. Step 2: Convert to fraction form
   512.69/681.38 = 681.38/x
3. Step 3: Cross multiply
   512.69x = 681.38 × 681.38
4. Step 4: Simplify right side
   512.69x = 464,271.89
5. Step 5: Solve for x
   x = 464,271.89/512.69
6. Step 6: Final answer
   x = 905.57