Finding the Third Proportional to 105,892 and 164,646

Step by Step Solution

1. Step 1: Write the proportion equation
   105,892 : 164,646 = 164,646 : x
2. Step 2: Convert to fraction form
   105,892/164,646 = 164,646/x
3. Step 3: Cross multiply
   105,892x = 164,646 × 164,646
4. Step 4: Simplify right side
   105,892x = 27,108,305,316
5. Step 5: Solve for x
   x = 27,108,305,316/105,892
6. Step 6: Final answer
   x = 255,999.56