Finding the Third Proportional to 86.54 and 189.69

Step by Step Solution

1. Step 1: Write the proportion equation
   86.54 : 189.69 = 189.69 : x
2. Step 2: Convert to fraction form
   86.54/189.69 = 189.69/x
3. Step 3: Cross multiply
   86.54x = 189.69 × 189.69
4. Step 4: Simplify right side
   86.54x = 35,980.61
5. Step 5: Solve for x
   x = 35,980.61/86.54
6. Step 6: Final answer
   x = 415.78