Finding the Third Proportional to 77.84 and 111.69

Step by Step Solution

1. Step 1: Write the proportion equation
   77.84 : 111.69 = 111.69 : x
2. Step 2: Convert to fraction form
   77.84/111.69 = 111.69/x
3. Step 3: Cross multiply
   77.84x = 111.69 × 111.69
4. Step 4: Simplify right side
   77.84x = 12,474.97
5. Step 5: Solve for x
   x = 12,474.97/77.84
6. Step 6: Final answer
   x = 160.27