Finding the Third Proportional to 1,256 and 1,688

Step by Step Solution

1. Step 1: Write the proportion equation
   1,256 : 1,688 = 1,688 : x
2. Step 2: Convert to fraction form
   1,256/1,688 = 1,688/x
3. Step 3: Cross multiply
   1,256x = 1,688 × 1,688
4. Step 4: Simplify right side
   1,256x = 2,849,344
5. Step 5: Solve for x
   x = 2,849,344/1,256
6. Step 6: Final answer
   x = 2,268.59