Finding the Third Proportional to 105,896 and 165,096

Step by Step Solution

1. Step 1: Write the proportion equation
   105,896 : 165,096 = 165,096 : x
2. Step 2: Convert to fraction form
   105,896/165,096 = 165,096/x
3. Step 3: Cross multiply
   105,896x = 165,096 × 165,096
4. Step 4: Simplify right side
   105,896x = 27,256,689,216
5. Step 5: Solve for x
   x = 27,256,689,216/105,896
6. Step 6: Final answer
   x = 257,391.11