Finding the Third Proportional to 6,584 and 10,466

Step by Step Solution

1. Step 1: Write the proportion equation
   6,584 : 10,466 = 10,466 : x
2. Step 2: Convert to fraction form
   6,584/10,466 = 10,466/x
3. Step 3: Cross multiply
   6,584x = 10,466 × 10,466
4. Step 4: Simplify right side
   6,584x = 109,537,156
5. Step 5: Solve for x
   x = 109,537,156/6,584
6. Step 6: Final answer
   x = 16,636.87