Finding the Third Proportional to 578.81 and 827.72

Step by Step Solution

1. Step 1: Write the proportion equation
   578.81 : 827.72 = 827.72 : x
2. Step 2: Convert to fraction form
   578.81/827.72 = 827.72/x
3. Step 3: Cross multiply
   578.81x = 827.72 × 827.72
4. Step 4: Simplify right side
   578.81x = 685,118.33
5. Step 5: Solve for x
   x = 685,118.33/578.81
6. Step 6: Final answer
   x = 1,183.66