Finding the Third Proportional to 546.48 and 823.86

Step by Step Solution

1. Step 1: Write the proportion equation
   546.48 : 823.86 = 823.86 : x
2. Step 2: Convert to fraction form
   546.48/823.86 = 823.86/x
3. Step 3: Cross multiply
   546.48x = 823.86 × 823.86
4. Step 4: Simplify right side
   546.48x = 678,749.50
5. Step 5: Solve for x
   x = 678,749.50/546.48
6. Step 6: Final answer
   x = 1,242.03