Finding the Third Proportional to 39.64 and 83.69

Step by Step Solution

1. Step 1: Write the proportion equation
   39.64 : 83.69 = 83.69 : x
2. Step 2: Convert to fraction form
   39.64/83.69 = 83.69/x
3. Step 3: Cross multiply
   39.64x = 83.69 × 83.69
4. Step 4: Simplify right side
   39.64x = 7,004.75
5. Step 5: Solve for x
   x = 7,004.75/39.64
6. Step 6: Final answer
   x = 176.69