Finding the Third Proportional to 106.50 and 175.69

Step by Step Solution

1. Step 1: Write the proportion equation
   106.50 : 175.69 = 175.69 : x
2. Step 2: Convert to fraction form
   106.50/175.69 = 175.69/x
3. Step 3: Cross multiply
   106.50x = 175.69 × 175.69
4. Step 4: Simplify right side
   106.50x = 30,866.10
5. Step 5: Solve for x
   x = 30,866.10/106.50
6. Step 6: Final answer
   x = 289.82