Finding the Third Proportional to 165.38 and 358.59

Step by Step Solution

1. Step 1: Write the proportion equation
   165.38 : 358.59 = 358.59 : x
2. Step 2: Convert to fraction form
   165.38/358.59 = 358.59/x
3. Step 3: Cross multiply
   165.38x = 358.59 × 358.59
4. Step 4: Simplify right side
   165.38x = 128,589.48
5. Step 5: Solve for x
   x = 128,589.48/165.38
6. Step 6: Final answer
   x = 777.56