Finding the Third Proportional to 684.56 and 1,414.69

Step by Step Solution

1. Step 1: Write the proportion equation
   684.56 : 1,414.69 = 1,414.69 : x
2. Step 2: Convert to fraction form
   684.56/1,414.69 = 1,414.69/x
3. Step 3: Cross multiply
   684.56x = 1,414.69 × 1,414.69
4. Step 4: Simplify right side
   684.56x = 2,001,340.72
5. Step 5: Solve for x
   x = 2,001,340.72/684.56
6. Step 6: Final answer
   x = 2,923.53