Finding the Third Proportional to 137.53 and 205.88

Step by Step Solution

1. Step 1: Write the proportion equation
   137.53 : 205.88 = 205.88 : x
2. Step 2: Convert to fraction form
   137.53/205.88 = 205.88/x
3. Step 3: Cross multiply
   137.53x = 205.88 × 205.88
4. Step 4: Simplify right side
   137.53x = 42,384.52
5. Step 5: Solve for x
   x = 42,384.52/137.53
6. Step 6: Final answer
   x = 308.18