Finding the Third Proportional to 2,577 and 5,640

Step by Step Solution

1. Step 1: Write the proportion equation
   2,577 : 5,640 = 5,640 : x
2. Step 2: Convert to fraction form
   2,577/5,640 = 5,640/x
3. Step 3: Cross multiply
   2,577x = 5,640 × 5,640
4. Step 4: Simplify right side
   2,577x = 31,809,600
5. Step 5: Solve for x
   x = 31,809,600/2,577
6. Step 6: Final answer
   x = 12,343.66