Finding the Third Proportional to 102,414 and 213,003

Step by Step Solution

1. Step 1: Write the proportion equation
   102,414 : 213,003 = 213,003 : x
2. Step 2: Convert to fraction form
   102,414/213,003 = 213,003/x
3. Step 3: Cross multiply
   102,414x = 213,003 × 213,003
4. Step 4: Simplify right side
   102,414x = 45,370,278,009
5. Step 5: Solve for x
   x = 45,370,278,009/102,414
6. Step 6: Final answer
   x = 443,008.55