Finding the Third Proportional to 2,538 and 5,886

Step by Step Solution

1. Step 1: Write the proportion equation
   2,538 : 5,886 = 5,886 : x
2. Step 2: Convert to fraction form
   2,538/5,886 = 5,886/x
3. Step 3: Cross multiply
   2,538x = 5,886 × 5,886
4. Step 4: Simplify right side
   2,538x = 34,644,996
5. Step 5: Solve for x
   x = 34,644,996/2,538
6. Step 6: Final answer
   x = 13,650.51