Answer:
The perimeter of triangle = 20.3
Step-by-step explanation:
We need to find perimeter of the triangle with vertices at (−2, 3), (3, 6), and (2, −2)
The formula used to find perimeter is: [tex]Perimeter=Sum\:of\:length\:of\:all\:sides[/tex]
First we need to find length of each side using distance formula:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Find distance between (−2, 3), (3, 6)
We have: [tex]x_1=-2,y_1=3, x_2=3,y_2=6[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(3-(-2))^2+(6-3)^2}\\Distance=\sqrt{(3+2)^2+(6-3)^2}\\Distance=\sqrt{(5)^2+(3)^2}\\Distance=\sqrt{25+9}\\Distance=\sqrt{34}\\Distance = 5.83[/tex]
So, The distance between (−2, 3), (3, 6) is 5.83
Find distance between (3, 6),(2,-2)
We have: [tex]x_1=3,y_1=6, x_2=2,y_2=-2[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(2-3)^2+(-2-6)^2}\\Distance=\sqrt{(1)^2+(-8)^2}\\Distance=\sqrt{1+64}\\Distance=\sqrt{65}\\Distance=8.06[/tex]
So, The distance between (3, 6),(2,-2) is 8.06
Find distance between (-2,3),(2,-2)
We have: [tex]x_1=-2,y_1=3, x_2=2,y_2=-2[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(2-(-2))^2+(-2-3)^2}\\Distance=\sqrt{(2+2)^2+(-2-3)^2}\\Distance=\sqrt{(4)^2+(5)^2}\\Distance=\sqrt{16+25}\\Distance=\sqrt{41} \\Distance=6.40[/tex]
So, The distance between (-2, 3),(2,-2) is 6.40
So, The length of side 1 = 5.83
The length of side 2 = 8.06
The length of side 3 = 6.40
The perimeter of triangle will be:
[tex]Perimeter=Sum\:of\:length\:of\:all\:sides\\Perimeter=5.83+8.06+6.40\\Perimeter=20.29\approx 20.3[/tex]
So, The perimeter of triangle = 20.3
