Finding the Third Proportional to 5,156 and 10,564

Step by Step Solution

1. Step 1: Write the proportion equation
   5,156 : 10,564 = 10,564 : x
2. Step 2: Convert to fraction form
   5,156/10,564 = 10,564/x
3. Step 3: Cross multiply
   5,156x = 10,564 × 10,564
4. Step 4: Simplify right side
   5,156x = 111,598,096
5. Step 5: Solve for x
   x = 111,598,096/5,156
6. Step 6: Final answer
   x = 21,644.32