Finding the Third Proportional to 37.69 and 82.41

Step by Step Solution

1. Step 1: Write the proportion equation
   37.69 : 82.41 = 82.41 : x
2. Step 2: Convert to fraction form
   37.69/82.41 = 82.41/x
3. Step 3: Cross multiply
   37.69x = 82.41 × 82.41
4. Step 4: Simplify right side
   37.69x = 6,790.79
5. Step 5: Solve for x
   x = 6,790.79/37.69
6. Step 6: Final answer
   x = 180.19