Finding the Third Proportional to 346.38 and 509.31

Step by Step Solution

1. Step 1: Write the proportion equation
   346.38 : 509.31 = 509.31 : x
2. Step 2: Convert to fraction form
   346.38/509.31 = 509.31/x
3. Step 3: Cross multiply
   346.38x = 509.31 × 509.31
4. Step 4: Simplify right side
   346.38x = 259,399.22
5. Step 5: Solve for x
   x = 259,399.22/346.38
6. Step 6: Final answer
   x = 748.90