Question

leilani uses an aerial view of the museums property boundaries as a reference to make a map. the polygon in leilanis map is a dilation of the polygon in the aerial view. what is the value of x, in centimeters? aerial view 9.6 cm 24 cm leilanis map 6.4 cm x

Explanation:

Step1: Find the scale - factor

Since the two polygons are dilations of each other, the ratios of corresponding sides are equal. Let's use the known corresponding sides. The ratio of the side lengths is $\frac{6.4}{9.6}=\frac{2}{3}$.

Step2: Calculate the value of $x$

Set up a proportion using the scale - factor. We know that $\frac{x}{24}=\frac{2}{3}$. Cross - multiply to get $3x = 24\times2$. Then $3x=48$, and $x = 16$.

Answer:

$16$