Finding the Third Proportional to 111.66 and 180.56

Step by Step Solution

1. Step 1: Write the proportion equation
   111.66 : 180.56 = 180.56 : x
2. Step 2: Convert to fraction form
   111.66/180.56 = 180.56/x
3. Step 3: Cross multiply
   111.66x = 180.56 × 180.56
4. Step 4: Simplify right side
   111.66x = 32,602.82
5. Step 5: Solve for x
   x = 32,602.82/111.66
6. Step 6: Final answer
   x = 291.99