Finding the Third Proportional to 165,870 and 257,256

Step by Step Solution

1. Step 1: Write the proportion equation
   165,870 : 257,256 = 257,256 : x
2. Step 2: Convert to fraction form
   165,870/257,256 = 257,256/x
3. Step 3: Cross multiply
   165,870x = 257,256 × 257,256
4. Step 4: Simplify right side
   165,870x = 66,180,649,536
5. Step 5: Solve for x
   x = 66,180,649,536/165,870
6. Step 6: Final answer
   x = 398,991.07