Finding the Third Proportional to 82,164 and 117,414

Step by Step Solution

1. Step 1: Write the proportion equation
   82,164 : 117,414 = 117,414 : x
2. Step 2: Convert to fraction form
   82,164/117,414 = 117,414/x
3. Step 3: Cross multiply
   82,164x = 117,414 × 117,414
4. Step 4: Simplify right side
   82,164x = 13,786,047,396
5. Step 5: Solve for x
   x = 13,786,047,396/82,164
6. Step 6: Final answer
   x = 167,786.96