Finding the Third Proportional to 142.50 and 178.13

Step by Step Solution

1. Step 1: Write the proportion equation
   142.50 : 178.13 = 178.13 : x
2. Step 2: Convert to fraction form
   142.50/178.13 = 178.13/x
3. Step 3: Cross multiply
   142.50x = 178.13 × 178.13
4. Step 4: Simplify right side
   142.50x = 31,728.52
5. Step 5: Solve for x
   x = 31,728.52/142.50
6. Step 6: Final answer
   x = 222.66