Finding the Third Proportional to 189.56 and 406.06

Step by Step Solution

1. Step 1: Write the proportion equation
   189.56 : 406.06 = 406.06 : x
2. Step 2: Convert to fraction form
   189.56/406.06 = 406.06/x
3. Step 3: Cross multiply
   189.56x = 406.06 × 406.06
4. Step 4: Simplify right side
   189.56x = 164,886.75
5. Step 5: Solve for x
   x = 164,886.75/189.56
6. Step 6: Final answer
   x = 869.83