Finding the Third Proportional to 109.50 and 256.13

Step by Step Solution

1. Step 1: Write the proportion equation
   109.50 : 256.13 = 256.13 : x
2. Step 2: Convert to fraction form
   109.50/256.13 = 256.13/x
3. Step 3: Cross multiply
   109.50x = 256.13 × 256.13
4. Step 4: Simplify right side
   109.50x = 65,600.02
5. Step 5: Solve for x
   x = 65,600.02/109.50
6. Step 6: Final answer
   x = 599.09