Finding the Third Proportional to 48 and 111

Step by Step Solution

1. Step 1: Write the proportion equation
   48 : 111 = 111 : x
2. Step 2: Convert to fraction form
   48/111 = 111/x
3. Step 3: Cross multiply
   48x = 111 × 111
4. Step 4: Simplify right side
   48x = 12,321
5. Step 5: Solve for x
   x = 12,321/48
6. Step 6: Final answer
   x = 256.69