Finding the Third Proportional to 117,566 and 256,111

Step by Step Solution

1. Step 1: Write the proportion equation
   117,566 : 256,111 = 256,111 : x
2. Step 2: Convert to fraction form
   117,566/256,111 = 256,111/x
3. Step 3: Cross multiply
   117,566x = 256,111 × 256,111
4. Step 4: Simplify right side
   117,566x = 65,592,844,321
5. Step 5: Solve for x
   x = 65,592,844,321/117,566
6. Step 6: Final answer
   x = 557,923.59