Answer: 25.6 units
Step-by-step explanation:
In the given picture , it can be seen that the triangle is passing through three points (-5,4) , (1,4) and (3, -4).
Using distance formula , we find the side -lengths of the triangle.
The distance between two points (a,b) and (c,d) is given by :_
[tex]D=\sqrt{(d-b)^2+(c-a)^2}[/tex]
The distance between two points (-5,4) and (1,4):
[tex]d_1=\sqrt{(4-4)^2+(1-(-5))^2}=\sqrt{0+(6)^2}=6\ units[/tex]
The distance between two points (1,4) and (3, -4).:
[tex]d_2=\sqrt{(-4-4)^2+(3-1)^2}\\\\=\sqrt{(-8)^2+(2)^2}\\\\=\sqrt{64+4}=\sqrt{68}\approx8.25\ units[/tex]
The distance between two points (-5,4) and (3, -4).:
[tex]d_3=\sqrt{(-4-4)^2+(3-(-5))^2}\\\\=\sqrt{(-8)^2+(8)^2}\\\\=\sqrt{64+64}=\sqrt{128}\approx11.31\ units[/tex]
Now, the perimeter of triangle =[tex]d_1+d_2+d_3[/tex]
[tex]=6+8.25+11.31=25.56\approx25.6\ unit[/tex] ( to the nearest tenth of a unit)
Hence, the perimeter of the triangle shown on the coordinate plane. = 25.6 units
