Question

what is the value of r?

Explanation:

Step1: Determine the scale factor

Since the two polygons are similar, we can find the scale factor by comparing the corresponding sides. The side of length 16 in Polygon P corresponds to the side of length 4 in Polygon Q. The scale factor \(k\) is \(\frac{4}{16}=\frac{1}{4}\).

Step2: Calculate the value of \(r\)

The side of length 8 in Polygon P corresponds to the side of length \(r\) in Polygon Q. Using the scale factor, we have \(r = 8\times\frac{1}{4}\).

Answer:

\(2\)