Finding the Third Proportional to 514.69 and 765.56

Step by Step Solution

1. Step 1: Write the proportion equation
   514.69 : 765.56 = 765.56 : x
2. Step 2: Convert to fraction form
   514.69/765.56 = 765.56/x
3. Step 3: Cross multiply
   514.69x = 765.56 × 765.56
4. Step 4: Simplify right side
   514.69x = 586,085.94
5. Step 5: Solve for x
   x = 586,085.94/514.69
6. Step 6: Final answer
   x = 1,138.72