Finding the Third Proportional to 514.27 and 784.27

Step by Step Solution

1. Step 1: Write the proportion equation
   514.27 : 784.27 = 784.27 : x
2. Step 2: Convert to fraction form
   514.27/784.27 = 784.27/x
3. Step 3: Cross multiply
   514.27x = 784.27 × 784.27
4. Step 4: Simplify right side
   514.27x = 615,072.57
5. Step 5: Solve for x
   x = 615,072.57/514.27
6. Step 6: Final answer
   x = 1,196.02