Respuesta :

ANSWER

P = 30

EXPLANATION

The perimeter of a triangle is the sum of the length of its sides.

This triangle is:

To find its perimeter we have to find the side lengths, that are the distance between each pair of points.

The length of side AB is:

[tex]\begin{gathered} AB=\sqrt[]{(4-(-8))^2+(-1-(-1))^2} \\ AB=\sqrt[]{(4+8)^2+0} \\ AB=\sqrt[]{12^2} \\ AB=12 \end{gathered}[/tex]

The length of side BC is:

[tex]\begin{gathered} BC=\sqrt[]{(4-4)^2+(-1-4)^2} \\ BC=\sqrt[]{0+5^2} \\ BC=5 \end{gathered}[/tex]

Finally, side AC is:

[tex]\begin{gathered} AC=\sqrt[]{(-8-4)^2+(-1-4)^2} \\ AC=\sqrt[]{12^2+5^2} \\ AC=\sqrt[]{144+25} \\ AC=\sqrt[]{169} \\ AC=13 \end{gathered}[/tex]

Finally, the perimeter of the triangle is:

[tex]\begin{gathered} P=AB+BC+AC \\ P=12+5+13 \\ P=30 \end{gathered}[/tex]

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