Question

the figure was created by repeatedly reflecting triangle nmp. what is the perimeter of the figure? 36 in 42 in 44 in 48 in figure may not be drawn to scale

Explanation:

Step1: Analyze the side lengths

The figure is created by reflecting triangle \( NMP \). The sides of the figure are composed of segments. The non - equal side in the basic triangle \( NMP \) is \( MP = 4\) in, and the equal sides are \( NM=NP = 8\) in.

Step2: Count the number of each type of side

When we consider the perimeter, we note that the side of length \( 4\) in appears \( 6\) times and the side of length \( 8\) in appears \( 3\) times. Using the formula for the perimeter \(P=\sum_{i = 1}^{n}l_{i}\), where \(l_{i}\) are the side lengths.

$$P=6\times4 + 3\times8$$

Step3: Calculate the perimeter

First, calculate \(6\times4=24\) and \(3\times8 = 24\). Then \(P=24 + 24\)

$$P = 48$$

Answer:

\(48\) in (the fourth option)