Answer:
[tex]\textsf{Perimeter}=14+\sqrt{106}[/tex]
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
Given vertices:
As vertices (1, 5) and (1, -4) have the same x-coordinate, the measure of the line segment connecting the two points is the difference between their y-coordinates:
[tex]\implies 5-(-4)=9[/tex]
As vertices (1, -4) and (-4, -4) have the same y-coordinate, the measure of the line segment connecting the two points is the difference between their x-coordinates:
[tex]\implies 1-(-4)=5[/tex]
Finally, to find the measure of the line segment connecting points (1, 5) and (-4, -4), use the distance formula:
[tex]\implies d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\implies d=\sqrt{(-4-1)^2+(-4-5)^2}[/tex]
[tex]\implies d=\sqrt{(-5)^2+(-9)^2}[/tex]
[tex]\implies d=\sqrt{25+81}[/tex]
[tex]\implies d=\sqrt{106}[/tex]
Therefore, the perimeter of the given triangle is the sum of the found side lengths:
[tex]\implies \textsf{Perimeter}=9+5+\sqrt{106}[/tex]
[tex]\implies \textsf{Perimeter}=14+\sqrt{106}[/tex]
