Finding the Third Proportional to 384.19 and 685.69

Step by Step Solution

1. Step 1: Write the proportion equation
   384.19 : 685.69 = 685.69 : x
2. Step 2: Convert to fraction form
   384.19/685.69 = 685.69/x
3. Step 3: Cross multiply
   384.19x = 685.69 × 685.69
4. Step 4: Simplify right side
   384.19x = 470,167.35
5. Step 5: Solve for x
   x = 470,167.35/384.19
6. Step 6: Final answer
   x = 1,223.80