Finding the Third Proportional to 653.81 and 828.56

Step by Step Solution

1. Step 1: Write the proportion equation
   653.81 : 828.56 = 828.56 : x
2. Step 2: Convert to fraction form
   653.81/828.56 = 828.56/x
3. Step 3: Cross multiply
   653.81x = 828.56 × 828.56
4. Step 4: Simplify right side
   653.81x = 686,515.82
5. Step 5: Solve for x
   x = 686,515.82/653.81
6. Step 6: Final answer
   x = 1,050.02