The base and the height of a parallelogram are multiplied by 6 . Which of the following describes the effect of this change on the perimeter?

To analyze the effect of multiplying the base and height of a parallelogram by 6 on its perimeter, we need to consider the properties of a parallelogram. 1. **Understanding the Perimeter of a Parallelogram:** The perimeter \( P \) of a parallelogram is given by the formula: \[ P = 2(b + h) \] where \( b \) is the length of the base and \( h \) is the height. 2. **Effect of Multiplying Base and Height:** If both the base and height are multiplied by 6, the new base \( b' \) and height \( h' \) will be: \[ b' = 6b \] \[ h' = 6h \] 3. **Calculating the New Perimeter:** The new perimeter \( P' \) will be: \[ P' = 2(b' + h') = 2(6b + 6h) = 2 \cdot 6(b + h) = 12(b + h) \] 4. **Comparing the New Perimeter to the Original:** The original perimeter was \( P = 2(b + h) \). The new perimeter is \( P' = 12(b + h) \). 5. **Conclusion:** The new perimeter is 6 times the original perimeter. Therefore, multiplying the base and height of a parallelogram by 6 results in the perimeter also being multiplied by 6. Thus, the effect of this change on the perimeter is that it is multiplied by 6.