Finding the Third Proportional to 586.69 and 820.22

Step by Step Solution

1. Step 1: Write the proportion equation
   586.69 : 820.22 = 820.22 : x
2. Step 2: Convert to fraction form
   586.69/820.22 = 820.22/x
3. Step 3: Cross multiply
   586.69x = 820.22 × 820.22
4. Step 4: Simplify right side
   586.69x = 672,758.80
5. Step 5: Solve for x
   x = 672,758.80/586.69
6. Step 6: Final answer
   x = 1,146.71