Finding the Third Proportional to 82.34 and 177.31

Step by Step Solution

1. Step 1: Write the proportion equation
   82.34 : 177.31 = 177.31 : x
2. Step 2: Convert to fraction form
   82.34/177.31 = 177.31/x
3. Step 3: Cross multiply
   82.34x = 177.31 × 177.31
4. Step 4: Simplify right side
   82.34x = 31,439.72
5. Step 5: Solve for x
   x = 31,439.72/82.34
6. Step 6: Final answer
   x = 381.81