Finding the Third Proportional to 5,200 and 12,406

Step by Step Solution

1. Step 1: Write the proportion equation
   5,200 : 12,406 = 12,406 : x
2. Step 2: Convert to fraction form
   5,200/12,406 = 12,406/x
3. Step 3: Cross multiply
   5,200x = 12,406 × 12,406
4. Step 4: Simplify right side
   5,200x = 153,908,836
5. Step 5: Solve for x
   x = 153,908,836/5,200
6. Step 6: Final answer
   x = 29,597.85