Finding the Third Proportional to 2,538 and 5,211

Step by Step Solution

1. Step 1: Write the proportion equation
   2,538 : 5,211 = 5,211 : x
2. Step 2: Convert to fraction form
   2,538/5,211 = 5,211/x
3. Step 3: Cross multiply
   2,538x = 5,211 × 5,211
4. Step 4: Simplify right side
   2,538x = 27,154,521
5. Step 5: Solve for x
   x = 27,154,521/2,538
6. Step 6: Final answer
   x = 10,699.18