Finding the Third Proportional to 1,686 and 3,456

Step by Step Solution

1. Step 1: Write the proportion equation
   1,686 : 3,456 = 3,456 : x
2. Step 2: Convert to fraction form
   1,686/3,456 = 3,456/x
3. Step 3: Cross multiply
   1,686x = 3,456 × 3,456
4. Step 4: Simplify right side
   1,686x = 11,943,936
5. Step 5: Solve for x
   x = 11,943,936/1,686
6. Step 6: Final answer
   x = 7,084.19