Finding the Third Proportional to 1,686 and 1,834

Step by Step Solution

1. Step 1: Write the proportion equation
   1,686 : 1,834 = 1,834 : x
2. Step 2: Convert to fraction form
   1,686/1,834 = 1,834/x
3. Step 3: Cross multiply
   1,686x = 1,834 × 1,834
4. Step 4: Simplify right side
   1,686x = 3,363,556
5. Step 5: Solve for x
   x = 3,363,556/1,686
6. Step 6: Final answer
   x = 1,994.99