Question

a polygon has perimeter 16. it is dilated with a scale factor of k, and the resulting image has a perimeter of 12. what is the scale factor? a $\frac{1}{4}$ b $\frac{2}{3}$ c $\frac{3}{4}$ d $\frac{4}{3}$

Explanation:

Step1: Recall dilation - perimeter relationship

The perimeter of a dilated polygon is the product of the original perimeter and the scale - factor. Let the original perimeter be $P_1 = 16$ and the dilated perimeter be $P_2 = 12$, and the scale - factor be $k$. So, $P_2=k\times P_1$.

Step2: Solve for the scale - factor

We have the equation $12 = k\times16$. To find $k$, we divide both sides of the equation by 16. So, $k=\frac{12}{16}=\frac{3}{4}$.

Answer:

C. $\frac{3}{4}$