Question

look at this parallelogram. if both dimensions are halved, then which of the following statements about its perimeter will be true? the new perimeter will be 2 times the old perimeter. the new perimeter will be 1/2 of the old perimeter. the new perimeter will be 4 times the old perimeter. the new perimeter will be 3 times the old perimeter.

Explanation:

Step1: Recall perimeter - change rule

The perimeter of a polygon is the sum of its side - lengths. If each side - length of a polygon is multiplied by a factor $k$, the new perimeter $P_{new}$ and the old perimeter $P_{old}$ are related by $P_{new}=k\times P_{old}$.

Step2: Identify the scaling factor

Here, the scaling factor $k = \frac{1}{2}$ since the dimensions are halved.

Step3: Calculate the new - perimeter relationship

Substitute $k=\frac{1}{2}$ into the formula $P_{new}=k\times P_{old}$. We get $P_{new}=\frac{1}{2}P_{old}$.

Answer:

The new perimeter will be $\frac{1}{2}$ of the old perimeter.