Finding the Third Proportional to 10,206 and 19,656

Step by Step Solution

1. Step 1: Write the proportion equation
   10,206 : 19,656 = 19,656 : x
2. Step 2: Convert to fraction form
   10,206/19,656 = 19,656/x
3. Step 3: Cross multiply
   10,206x = 19,656 × 19,656
4. Step 4: Simplify right side
   10,206x = 386,358,336
5. Step 5: Solve for x
   x = 386,358,336/10,206
6. Step 6: Final answer
   x = 37,856