Question

Examine the diagram and information to answer the question.

Answer 1

Answer:

23.4 units

Step-by-step explanation:

Given the point of the vertices of triangle ABC as A(−5,1), B(2,1), and C(6,4).

The distance (d) between two points X (x₁ , y₁) and Y(x₂, y₂) is given as:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. We can use this to calculate the length of the sides of the triangle. Therefore:

$AB=\sqrt{(2-(-5))^2+(1-1)^2}=\sqrt{7^2}=7\\ AC=\sqrt{(6-(-5))^2+(4-1)^2}=\sqrt{11^2+3^2}=11.4\\\\BC=\sqrt{(6-(2))^2+(4-1)^2}=\sqrt{4^2+3^2}=5$

The perimeter of the triangle ABC = AB + AC + BC = 7 + 11.4 + 5 = 23.4 units