Finding the Third Proportional to 456.88 and 706.69

Step by Step Solution

1. Step 1: Write the proportion equation
   456.88 : 706.69 = 706.69 : x
2. Step 2: Convert to fraction form
   456.88/706.69 = 706.69/x
3. Step 3: Cross multiply
   456.88x = 706.69 × 706.69
4. Step 4: Simplify right side
   456.88x = 499,407.22
5. Step 5: Solve for x
   x = 499,407.22/456.88
6. Step 6: Final answer
   x = 1,093.09