Question

find the perimeter of the triangle whose vertices are (-4, - 3), (8, - 3), and (8,2). write the exact answer. do not round.

Explanation:

Step1: Find length of first side

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $(-4,-3)$ and $(8,-3)$, $x_1=-4,y_1 = - 3,x_2=8,y_2=-3$. Then $d_1=\sqrt{(8 - (-4))^2+(-3-(-3))^2}=\sqrt{(8 + 4)^2+0^2}=\sqrt{12^2}=12$.

Step2: Find length of second side

For points $(8,-3)$ and $(8,2)$, $x_1 = 8,y_1=-3,x_2=8,y_2 = 2$. Then $d_2=\sqrt{(8 - 8)^2+(2-(-3))^2}=\sqrt{0^2+5^2}=5$.

Step3: Find length of third side

For points $(-4,-3)$ and $(8,2)$, $x_1=-4,y_1=-3,x_2=8,y_2 = 2$. Then $d_3=\sqrt{(8-(-4))^2+(2 - (-3))^2}=\sqrt{(8 + 4)^2+(2 + 3)^2}=\sqrt{12^2+5^2}=\sqrt{144 + 25}=\sqrt{169}=13$.

Step4: Calculate perimeter

Perimeter $P=d_1 + d_2+d_3=12 + 5+13=30$.

Answer:

30