Question

polygon q is a scaled copy of polygon p.
what is the value of r?

Explanation:

Step1: Find the scale factor

Since polygon \(Q\) is a scaled - copy of polygon \(P\), we can find the scale factor by comparing corresponding sides. The side of length \(12\) in polygon \(P\) corresponds to the side of length \(3\) in polygon \(Q\).
The scale factor \(k=\frac{3}{12}=\frac{1}{4}\)

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 \(k = \frac{1}{4}\), we have \(r=8\times k\)
Substitute \(k=\frac{1}{4}\) into the equation: \(r = 8\times\frac{1}{4}\)
\(r = 2\)

Answer:

\(2\)