Finding the Third Proportional to 13.80 and 31.72

Step by Step Solution

1. Step 1: Write the proportion equation
   13.80 : 31.72 = 31.72 : x
2. Step 2: Convert to fraction form
   13.80/31.72 = 31.72/x
3. Step 3: Cross multiply
   13.80x = 31.72 × 31.72
4. Step 4: Simplify right side
   13.80x = 1,006.14
5. Step 5: Solve for x
   x = 1,006.14/13.80
6. Step 6: Final answer
   x = 72.89