Finding the Third Proportional to 2,538 and 5,814

Step by Step Solution

1. Step 1: Write the proportion equation
   2,538 : 5,814 = 5,814 : x
2. Step 2: Convert to fraction form
   2,538/5,814 = 5,814/x
3. Step 3: Cross multiply
   2,538x = 5,814 × 5,814
4. Step 4: Simplify right side
   2,538x = 33,802,596
5. Step 5: Solve for x
   x = 33,802,596/2,538
6. Step 6: Final answer
   x = 13,318.60