Answer:
The perimeter of the triangle is 8.83 km
Explanation:
Given:
2) Triangle ABC with sides AB, BC and CA
To find:
The perimeter of the triangle using the distance formula
To determine the perimeter, we need to first find the 3 sides of the triangle. To do this, the distance formula will be used:
[tex]$dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}$[/tex]
A = (0, 0), B = (3.5, 0) and C = (2, -2)
[tex]\begin{gathered} Distance\text{ AB: A = \lparen0, 0\rparen, B = \lparen3.5, 0\rparen} \\ dis\tan ce\text{ AB = }\sqrt{(0-0)^2+(3.5-0)^2}\text{ = }\sqrt{0\text{ + 12.25}} \\ distance\text{ AB = 3.5} \end{gathered}[/tex][tex]\begin{gathered} Distance\text{ BC: B = \lparen3.5, 0\rparen and C = \lparen2, -2\rparen} \\ dis\tan ce\text{ = }\sqrt{(-2-0)^2+(2-3.5)^2}\text{ = }\sqrt{(-2)^2+(-1.5)^2} \\ distance\text{ = }\sqrt{4\text{ + 2.25}}\text{ = }\sqrt{6.25} \\ distance\text{ = 2.5} \end{gathered}[/tex][tex]\begin{gathered} Distance\text{ CA = C = \lparen2, -2\rparen and A = \lparen0, 0\rparen} \\ dis\tan ce\text{ CA = }\sqrt{(0-(-2))^2+(0-2)^2}\text{ = }\sqrt{(0+2)^2+(-2)^2} \\ distance\text{ CA}=\text{ }\sqrt{4+4}\text{ = }\sqrt{8} \\ distance\text{ CA = 2.83} \end{gathered}[/tex]
The perimeter of the triangle = sum of all 3 sides
[tex]\begin{gathered} Perimeter\text{ = AB + BC + CA} \\ Perimeter\text{ of the triangle = 3.5 + 2.5 + 2.83} \\ \\ The\text{ perimeter of the triangle = 8.83 km} \end{gathered}[/tex]
