Finding the Third Proportional to 111.38 and 256.69

Step by Step Solution

1. Step 1: Write the proportion equation
   111.38 : 256.69 = 256.69 : x
2. Step 2: Convert to fraction form
   111.38/256.69 = 256.69/x
3. Step 3: Cross multiply
   111.38x = 256.69 × 256.69
4. Step 4: Simplify right side
   111.38x = 65,888.47
5. Step 5: Solve for x
   x = 65,888.47/111.38
6. Step 6: Final answer
   x = 591.59