Finding the Third Proportional to 686.81 and 1,648.69

Step by Step Solution

1. Step 1: Write the proportion equation
   686.81 : 1,648.69 = 1,648.69 : x
2. Step 2: Convert to fraction form
   686.81/1,648.69 = 1,648.69/x
3. Step 3: Cross multiply
   686.81x = 1,648.69 × 1,648.69
4. Step 4: Simplify right side
   686.81x = 2,718,170.47
5. Step 5: Solve for x
   x = 2,718,170.47/686.81
6. Step 6: Final answer
   x = 3,957.66