Finding the Third Proportional to 405.38 and 577.69

Step by Step Solution

1. Step 1: Write the proportion equation
   405.38 : 577.69 = 577.69 : x
2. Step 2: Convert to fraction form
   405.38/577.69 = 577.69/x
3. Step 3: Cross multiply
   405.38x = 577.69 × 577.69
4. Step 4: Simplify right side
   405.38x = 333,722.85
5. Step 5: Solve for x
   x = 333,722.85/405.38
6. Step 6: Final answer
   x = 823.24