Finding the Third Proportional to 2,186.16 and 4,564.69

Step by Step Solution

1. Step 1: Write the proportion equation
   2,186.16 : 4,564.69 = 4,564.69 : x
2. Step 2: Convert to fraction form
   2,186.16/4,564.69 = 4,564.69/x
3. Step 3: Cross multiply
   2,186.16x = 4,564.69 × 4,564.69
4. Step 4: Simplify right side
   2,186.16x = 20,836,371.97
5. Step 5: Solve for x
   x = 20,836,371.97/2,186.16
6. Step 6: Final answer
   x = 9,531.05