Finding the Third Proportional to 165.38 and 255.88

Step by Step Solution

1. Step 1: Write the proportion equation
   165.38 : 255.88 = 255.88 : x
2. Step 2: Convert to fraction form
   165.38/255.88 = 255.88/x
3. Step 3: Cross multiply
   165.38x = 255.88 × 255.88
4. Step 4: Simplify right side
   165.38x = 65,472.02
5. Step 5: Solve for x
   x = 65,472.02/165.38
6. Step 6: Final answer
   x = 395.90