Finding the Third Proportional to 123.56 and 177.56

Step by Step Solution

1. Step 1: Write the proportion equation
   123.56 : 177.56 = 177.56 : x
2. Step 2: Convert to fraction form
   123.56/177.56 = 177.56/x
3. Step 3: Cross multiply
   123.56x = 177.56 × 177.56
4. Step 4: Simplify right side
   123.56x = 31,528.44
5. Step 5: Solve for x
   x = 31,528.44/123.56
6. Step 6: Final answer
   x = 255.16