Finding the Third Proportional to 256.50 and 401.63

Step by Step Solution

1. Step 1: Write the proportion equation
   256.50 : 401.63 = 401.63 : x
2. Step 2: Convert to fraction form
   256.50/401.63 = 401.63/x
3. Step 3: Cross multiply
   256.50x = 401.63 × 401.63
4. Step 4: Simplify right side
   256.50x = 161,302.64
5. Step 5: Solve for x
   x = 161,302.64/256.50
6. Step 6: Final answer
   x = 628.86