Question

Find the perimeter of the triangle with vertices D(−2, −1), E(3, 2), and F(0, 4). Do not round before calculating the perimeter. After calculating the perimeter, round your answer to the nearest tenth.

Answer 1

Answer:
`15.3\ \text{units}`

Explanation:

Given

Coordinates of the corners are D(-2,-1), E(3,2), and F(0,4)

Length DE is

`\Rightarrow DE=√((2+1)^2+(3+2)^2)\\\Rightarrow DE=√((3)^2+(5)^2)\\\Rightarrow DE=√(34)\ \text{units}`

Length EF is

`\Rightarrow EF=√((4-2)^2+(0-3)^2)\\\Rightarrow EF=√((2)^2+(-3)^2)\\\Rightarrow EF=√(13)\ \text{units}`

Length FD is

`\Rightarrow FD=√((4+1)^2+(0+2)^2)\\\Rightarrow FD=√((5)^2+(2)^2)\\\Rightarrow FD=√(29)\ \text{units}`

Perimeter of the triangle is

`\Rightarrow DE+EF+FD=√(34)+√(17)+√(29)\\\Rightarrow DE+EF+FD=15.3\ \text{units}`