Finding the Third Proportional to 265.78 and 407.53

Step by Step Solution

1. Step 1: Write the proportion equation
   265.78 : 407.53 = 407.53 : x
2. Step 2: Convert to fraction form
   265.78/407.53 = 407.53/x
3. Step 3: Cross multiply
   265.78x = 407.53 × 407.53
4. Step 4: Simplify right side
   265.78x = 166,081.72
5. Step 5: Solve for x
   x = 166,081.72/265.78
6. Step 6: Final answer
   x = 624.88