Question

the length of each side of parallelogram rstu is multiplied by three to create parallelogram wxyz. what is the ratio of the area of parallelogram rstu to the area of parallelogram wxyz?
a 1:3
b 1:6
c 1:9
d 1:27
e 1:81

Explanation:

Step1: Recall area formula for parallelogram

The area of a parallelogram is $A = base\times height$, denoted as $A_1 = b_1\times h_1$ for parallelogram $RSTU$.

Step2: Analyze side - length change

When each side of parallelogram $RSTU$ is multiplied by 3 to get parallelogram $WXYZ$, both the base and the height of the new parallelogram are 3 times the original. So for parallelogram $WXYZ$, $b_2 = 3b_1$ and $h_2=3h_1$, and its area $A_2=b_2\times h_2=(3b_1)\times(3h_1) = 9b_1h_1$.

Step3: Find the ratio of areas

The ratio of the area of parallelogram $RSTU$ to the area of parallelogram $WXYZ$ is $\frac{A_1}{A_2}=\frac{b_1h_1}{9b_1h_1}=\frac{1}{9}$.

Answer:

C. $1:9$