Finding the Third Proportional to 106.50 and 165.38

Step by Step Solution

1. Step 1: Write the proportion equation
   106.50 : 165.38 = 165.38 : x
2. Step 2: Convert to fraction form
   106.50/165.38 = 165.38/x
3. Step 3: Cross multiply
   106.50x = 165.38 × 165.38
4. Step 4: Simplify right side
   106.50x = 27,348.89
5. Step 5: Solve for x
   x = 27,348.89/106.50
6. Step 6: Final answer
   x = 256.80