Finding the Third Proportional to 37.81 and 82.56

Step by Step Solution

1. Step 1: Write the proportion equation
   37.81 : 82.56 = 82.56 : x
2. Step 2: Convert to fraction form
   37.81/82.56 = 82.56/x
3. Step 3: Cross multiply
   37.81x = 82.56 × 82.56
4. Step 4: Simplify right side
   37.81x = 6,816.57
5. Step 5: Solve for x
   x = 6,816.57/37.81
6. Step 6: Final answer
   x = 180.27