Finding the Third Proportional to 105.19 and 137.53

Step by Step Solution

1. Step 1: Write the proportion equation
   105.19 : 137.53 = 137.53 : x
2. Step 2: Convert to fraction form
   105.19/137.53 = 137.53/x
3. Step 3: Cross multiply
   105.19x = 137.53 × 137.53
4. Step 4: Simplify right side
   105.19x = 18,914.84
5. Step 5: Solve for x
   x = 18,914.84/105.19
6. Step 6: Final answer
   x = 179.82