Finding the Third Proportional to 4,656 and 5,648

Step by Step Solution

1. Step 1: Write the proportion equation
   4,656 : 5,648 = 5,648 : x
2. Step 2: Convert to fraction form
   4,656/5,648 = 5,648/x
3. Step 3: Cross multiply
   4,656x = 5,648 × 5,648
4. Step 4: Simplify right side
   4,656x = 31,899,904
5. Step 5: Solve for x
   x = 31,899,904/4,656
6. Step 6: Final answer
   x = 6,851.35