Question

polygon q is a scaled copy of polygon p.
(image of polygon p with side lengths 16, 8, 12 and polygon q with side lengths 4, r, 3)
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 using the corresponding sides. Let's use the sides of length \(12\) (in polygon \(P\)) and \(3\) (in polygon \(Q\)).
The scale factor \(k=\frac{\text{side in }Q}{\text{side in }P}\)
\(k = \frac{3}{12}=\frac{1}{4}\)

Step2: Calculate the value of \(r\)

We know that the side of length \(8\) in polygon \(P\) corresponds to the side of length \(r\) in polygon \(Q\).
Using the formula \(r=8\times k\) (because \(r\) (side in \(Q\)) \(=\) side in \(P\times\) scale factor)
Substitute \(k = \frac{1}{4}\) into the formula: \(r=8\times\frac{1}{4}\)
\(r = 2\)

Answer:

\(2\)