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: $15.3\ \text{units}$

Step-by-step explanation:

Given

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

Length DE is

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

Length EF is

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

Length FD is

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

Perimeter of the triangle is

$\Rightarrow DE+EF+FD=\sqrt{34}+\sqrt{17}+\sqrt{29}\\\Rightarrow DE+EF+FD=15.3\ \text{units}$