Finding the Third Proportional to 2,538 and 5,896

Step by Step Solution

1. Step 1: Write the proportion equation
   2,538 : 5,896 = 5,896 : x
2. Step 2: Convert to fraction form
   2,538/5,896 = 5,896/x
3. Step 3: Cross multiply
   2,538x = 5,896 × 5,896
4. Step 4: Simplify right side
   2,538x = 34,762,816
5. Step 5: Solve for x
   x = 34,762,816/2,538
6. Step 6: Final answer
   x = 13,696.93