Finding the Third Proportional to 106.50 and 275.69

Step by Step Solution

1. Step 1: Write the proportion equation
   106.50 : 275.69 = 275.69 : x
2. Step 2: Convert to fraction form
   106.50/275.69 = 275.69/x
3. Step 3: Cross multiply
   106.50x = 275.69 × 275.69
4. Step 4: Simplify right side
   106.50x = 76,003.60
5. Step 5: Solve for x
   x = 76,003.60/106.50
6. Step 6: Final answer
   x = 713.65