Question

polygon q is a scaled copy of polygon p.
diagram: polygon p (with a side labeled 8, another 16, another 12) and polygon q (with a side labeled 4, another 3, and ( r ))
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. Let's take the side of length 12 in P and 3 in Q. The scale factor \( k \) is \( \frac{3}{12}=\frac{1}{4} \). Alternatively, using the side 16 in P and 4 in Q: \( \frac{4}{16}=\frac{1}{4} \), so the scale factor is \( \frac{1}{4} \).

Step2: Calculate \( r \)

The side of length 8 in P corresponds to side \( r \) in Q. Using the scale factor, \( r = 8\times\frac{1}{4} \)
\( r = 2 \)

Answer:

2