Question

analyze find the perimeter of equilateral triangle klm given the vertices k (-2, 1) and m (10, 6). explain your reasoning. perimeter = units. an equilateral triangle has congruent side lengths. use the distance formula to find km = 13. so, p = 39 (km) = units.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $K(-2,1)$ and $M(10,6)$, we have $x_1=-2,y_1 = 1,x_2=10,y_2 = 6$.
$$d_{KM}=\sqrt{(10-(-2))^2+(6 - 1)^2}=\sqrt{(10 + 2)^2+5^2}=\sqrt{144 + 25}=\sqrt{169}=13$$

Step2: Calculate perimeter of equilateral triangle

Since $\triangle KLM$ is equilateral, all side - lengths are equal. Let the side - length of the equilateral triangle be $s$. Here $s = KM=13$. The perimeter $P$ of an equilateral triangle is $P = 3s$. So $P=3\times13 = 39$.

Answer:

39