Finding the Third Proportional to 102,144 and 164,016

Step by Step Solution

1. Step 1: Write the proportion equation
   102,144 : 164,016 = 164,016 : x
2. Step 2: Convert to fraction form
   102,144/164,016 = 164,016/x
3. Step 3: Cross multiply
   102,144x = 164,016 × 164,016
4. Step 4: Simplify right side
   102,144x = 26,901,248,256
5. Step 5: Solve for x
   x = 26,901,248,256/102,144
6. Step 6: Final answer
   x = 263,365.92