Finding the Third Proportional to 501.75 and 729.69

Step by Step Solution

1. Step 1: Write the proportion equation
   501.75 : 729.69 = 729.69 : x
2. Step 2: Convert to fraction form
   501.75/729.69 = 729.69/x
3. Step 3: Cross multiply
   501.75x = 729.69 × 729.69
4. Step 4: Simplify right side
   501.75x = 532,443.85
5. Step 5: Solve for x
   x = 532,443.85/501.75
6. Step 6: Final answer
   x = 1,061.17