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. 6 in. 8 in. 4 in. figure may not be drawn to scale

Explanation:

Step1: Identify side - lengths

The figure is composed of congruent sides from the repeated reflection of triangle NMP. By observing, we can count the outer - side lengths. The lengths of the sides of the original triangle are 4 in, 6 in, and 8 in.

Step2: Count the outer - side lengths

Count the number of each side - length that contribute to the perimeter. After counting, we find that the perimeter is composed of 4 sides of length 4 in, 4 sides of length 6 in, and 4 sides of length 8 in.

Step3: Calculate the perimeter

The perimeter \(P=(4\times4 + 4\times6+4\times8)\) in. First, calculate \(4\times4 = 16\), \(4\times6 = 24\), and \(4\times8 = 32\). Then \(P=16 + 24+32=48\) in.

Answer:

48 in.