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 = . so, p = (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 $x_1=-2,y_1 = 1,x_2=10,y_2 = 6$.

Step2: Calculate $KM$

$KM=\sqrt{(10-(-2))^2+(6 - 1)^2}=\sqrt{(12)^2+(5)^2}=\sqrt{144 + 25}=\sqrt{169}=13$.

Step3: Calculate perimeter of equilateral - triangle

Since an equilateral triangle has all sides equal and perimeter $P$ of an equilateral triangle with side - length $s$ is $P = 3s$. Here $s=KM$, so $P = 3\times13=39$.

Answer:

$KM = 13$, $P=39$