Finding the Third Proportional to 144 and 256.50

Step by Step Solution

1. Step 1: Write the proportion equation
   144 : 256.50 = 256.50 : x
2. Step 2: Convert to fraction form
   144/256.50 = 256.50/x
3. Step 3: Cross multiply
   144x = 256.50 × 256.50
4. Step 4: Simplify right side
   144x = 65,792.25
5. Step 5: Solve for x
   x = 65,792.25/144
6. Step 6: Final answer
   x = 456.89