Finding the Third Proportional to 4,768 and 10,564

Step by Step Solution

1. Step 1: Write the proportion equation
   4,768 : 10,564 = 10,564 : x
2. Step 2: Convert to fraction form
   4,768/10,564 = 10,564/x
3. Step 3: Cross multiply
   4,768x = 10,564 × 10,564
4. Step 4: Simplify right side
   4,768x = 111,598,096
5. Step 5: Solve for x
   x = 111,598,096/4,768
6. Step 6: Final answer
   x = 23,405.64