Finding the Third Proportional to 165.38 and 259.50

Step by Step Solution

1. Step 1: Write the proportion equation
   165.38 : 259.50 = 259.50 : x
2. Step 2: Convert to fraction form
   165.38/259.50 = 259.50/x
3. Step 3: Cross multiply
   165.38x = 259.50 × 259.50
4. Step 4: Simplify right side
   165.38x = 67,340.25
5. Step 5: Solve for x
   x = 67,340.25/165.38
6. Step 6: Final answer
   x = 407.20