Finding the Third Proportional to 378.56 and 856.69

Step by Step Solution

1. Step 1: Write the proportion equation
   378.56 : 856.69 = 856.69 : x
2. Step 2: Convert to fraction form
   378.56/856.69 = 856.69/x
3. Step 3: Cross multiply
   378.56x = 856.69 × 856.69
4. Step 4: Simplify right side
   378.56x = 733,913.47
5. Step 5: Solve for x
   x = 733,913.47/378.56
6. Step 6: Final answer
   x = 1,938.69