Finding the Third Proportional to 1,414.13 and 3,697.31

Step by Step Solution

1. Step 1: Write the proportion equation
   1,414.13 : 3,697.31 = 3,697.31 : x
2. Step 2: Convert to fraction form
   1,414.13/3,697.31 = 3,697.31/x
3. Step 3: Cross multiply
   1,414.13x = 3,697.31 × 3,697.31
4. Step 4: Simplify right side
   1,414.13x = 13,670,119.72
5. Step 5: Solve for x
   x = 13,670,119.72/1,414.13
6. Step 6: Final answer
   x = 9,666.84