Finding the Third Proportional to 102 and 152.25

Step by Step Solution

1. Step 1: Write the proportion equation
   102 : 152.25 = 152.25 : x
2. Step 2: Convert to fraction form
   102/152.25 = 152.25/x
3. Step 3: Cross multiply
   102x = 152.25 × 152.25
4. Step 4: Simplify right side
   102x = 23,180.06
5. Step 5: Solve for x
   x = 23,180.06/102
6. Step 6: Final answer
   x = 227.26