Finding the Third Proportional to 199.69 and 414.56

Step by Step Solution

1. Step 1: Write the proportion equation
   199.69 : 414.56 = 414.56 : x
2. Step 2: Convert to fraction form
   199.69/414.56 = 414.56/x
3. Step 3: Cross multiply
   199.69x = 414.56 × 414.56
4. Step 4: Simplify right side
   199.69x = 171,862.07
5. Step 5: Solve for x
   x = 171,862.07/199.69
6. Step 6: Final answer
   x = 860.66