Finding the Third Proportional to 37.97 and 82.69

Step by Step Solution

1. Step 1: Write the proportion equation
   37.97 : 82.69 = 82.69 : x
2. Step 2: Convert to fraction form
   37.97/82.69 = 82.69/x
3. Step 3: Cross multiply
   37.97x = 82.69 × 82.69
4. Step 4: Simplify right side
   37.97x = 6,837.22
5. Step 5: Solve for x
   x = 6,837.22/37.97
6. Step 6: Final answer
   x = 180.08