Finding the Third Proportional to 2,591 and 5,665

Step by Step Solution

1. Step 1: Write the proportion equation
   2,591 : 5,665 = 5,665 : x
2. Step 2: Convert to fraction form
   2,591/5,665 = 5,665/x
3. Step 3: Cross multiply
   2,591x = 5,665 × 5,665
4. Step 4: Simplify right side
   2,591x = 32,092,225
5. Step 5: Solve for x
   x = 32,092,225/2,591
6. Step 6: Final answer
   x = 12,386.04