Finding the Third Proportional to 1,686 and 2,256

Step by Step Solution

1. Step 1: Write the proportion equation
   1,686 : 2,256 = 2,256 : x
2. Step 2: Convert to fraction form
   1,686/2,256 = 2,256/x
3. Step 3: Cross multiply
   1,686x = 2,256 × 2,256
4. Step 4: Simplify right side
   1,686x = 5,089,536
5. Step 5: Solve for x
   x = 5,089,536/1,686
6. Step 6: Final answer
   x = 3,018.70