Finding the Third Proportional to 37.78 and 89.63

Step by Step Solution

1. Step 1: Write the proportion equation
   37.78 : 89.63 = 89.63 : x
2. Step 2: Convert to fraction form
   37.78/89.63 = 89.63/x
3. Step 3: Cross multiply
   37.78x = 89.63 × 89.63
4. Step 4: Simplify right side
   37.78x = 8,032.64
5. Step 5: Solve for x
   x = 8,032.64/37.78
6. Step 6: Final answer
   x = 212.61