Finding the Third Proportional to 397.69 and 451.69

Step by Step Solution

1. Step 1: Write the proportion equation
   397.69 : 451.69 = 451.69 : x
2. Step 2: Convert to fraction form
   397.69/451.69 = 451.69/x
3. Step 3: Cross multiply
   397.69x = 451.69 × 451.69
4. Step 4: Simplify right side
   397.69x = 204,021.60
5. Step 5: Solve for x
   x = 204,021.60/397.69
6. Step 6: Final answer
   x = 513.02