Finding the Third Proportional to 37.69 and 82.13

Step by Step Solution

1. Step 1: Write the proportion equation
   37.69 : 82.13 = 82.13 : x
2. Step 2: Convert to fraction form
   37.69/82.13 = 82.13/x
3. Step 3: Cross multiply
   37.69x = 82.13 × 82.13
4. Step 4: Simplify right side
   37.69x = 6,744.52
5. Step 5: Solve for x
   x = 6,744.52/37.69
6. Step 6: Final answer
   x = 178.96