Finding the Third Proportional to 2,138 and 5,633

Step by Step Solution

1. Step 1: Write the proportion equation
   2,138 : 5,633 = 5,633 : x
2. Step 2: Convert to fraction form
   2,138/5,633 = 5,633/x
3. Step 3: Cross multiply
   2,138x = 5,633 × 5,633
4. Step 4: Simplify right side
   2,138x = 31,730,689
5. Step 5: Solve for x
   x = 31,730,689/2,138
6. Step 6: Final answer
   x = 14,841.30