Finding the Third Proportional to 213.57 and 465.59

Step by Step Solution

1. Step 1: Write the proportion equation
   213.57 : 465.59 = 465.59 : x
2. Step 2: Convert to fraction form
   213.57/465.59 = 465.59/x
3. Step 3: Cross multiply
   213.57x = 465.59 × 465.59
4. Step 4: Simplify right side
   213.57x = 216,775.72
5. Step 5: Solve for x
   x = 216,775.72/213.57
6. Step 6: Final answer
   x = 1,014.99