Finding the Third Proportional to 105,898 and 165,099

Step by Step Solution

1. Step 1: Write the proportion equation
   105,898 : 165,099 = 165,099 : x
2. Step 2: Convert to fraction form
   105,898/165,099 = 165,099/x
3. Step 3: Cross multiply
   105,898x = 165,099 × 165,099
4. Step 4: Simplify right side
   105,898x = 27,257,679,801
5. Step 5: Solve for x
   x = 27,257,679,801/105,898
6. Step 6: Final answer
   x = 257,395.61