Question

what is the perimeter of △efg? perimeter = units

Explanation:

Step1: Find the lengths of the sides using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Let $E(4,-4)$, $F(-8,-9)$, $G(-8,-4)$.
Length of $EF$:
$d_{EF}=\sqrt{(4 + 8)^2+(-4 + 9)^2}=\sqrt{12^2+5^2}=\sqrt{144 + 25}=\sqrt{169}=13$.

Step2: Find the length of $FG$.

Since $F(-8,-9)$ and $G(-8,-4)$, $x$-coordinates are the same.
$d_{FG}=\vert-4-(-9)\vert=\vert-4 + 9\vert = 5$.

Step3: Find the length of $GE$.

Since $G(-8,-4)$ and $E(4,-4)$, $y$-coordinates are the same.
$d_{GE}=\vert4-(-8)\vert=\vert4 + 8\vert=12$.

Step4: Calculate the perimeter.

Perimeter of $\triangle EFG=d_{EF}+d_{FG}+d_{GE}=13 + 5+12 = 30$.

Answer:

30