Finding the Third Proportional to 145.88 and 205.69

Step by Step Solution

1. Step 1: Write the proportion equation
   145.88 : 205.69 = 205.69 : x
2. Step 2: Convert to fraction form
   145.88/205.69 = 205.69/x
3. Step 3: Cross multiply
   145.88x = 205.69 × 205.69
4. Step 4: Simplify right side
   145.88x = 42,307.35
5. Step 5: Solve for x
   x = 42,307.35/145.88
6. Step 6: Final answer
   x = 290.02