Finding the Third Proportional to 2,586 and 5,664

Step by Step Solution

1. Step 1: Write the proportion equation
   2,586 : 5,664 = 5,664 : x
2. Step 2: Convert to fraction form
   2,586/5,664 = 5,664/x
3. Step 3: Cross multiply
   2,586x = 5,664 × 5,664
4. Step 4: Simplify right side
   2,586x = 32,080,896
5. Step 5: Solve for x
   x = 32,080,896/2,586
6. Step 6: Final answer
   x = 12,405.61