Finding the Third Proportional to 6,689 and 10,406

Step by Step Solution

1. Step 1: Write the proportion equation
   6,689 : 10,406 = 10,406 : x
2. Step 2: Convert to fraction form
   6,689/10,406 = 10,406/x
3. Step 3: Cross multiply
   6,689x = 10,406 × 10,406
4. Step 4: Simplify right side
   6,689x = 108,284,836
5. Step 5: Solve for x
   x = 108,284,836/6,689
6. Step 6: Final answer
   x = 16,188.49