Finding the Third Proportional to 586.94 and 820.56

Step by Step Solution

1. Step 1: Write the proportion equation
   586.94 : 820.56 = 820.56 : x
2. Step 2: Convert to fraction form
   586.94/820.56 = 820.56/x
3. Step 3: Cross multiply
   586.94x = 820.56 × 820.56
4. Step 4: Simplify right side
   586.94x = 673,322.82
5. Step 5: Solve for x
   x = 673,322.82/586.94
6. Step 6: Final answer
   x = 1,147.18