Question

Find the perimeter of a triangle with vertices of (-8,-1),(4,-1), and (4,4) , exact answer don't round up

Answer 1

P = 30

Step-by-step 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:

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

The length of side BC is:

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

Finally, side AC is:

`\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}`

Finally, the perimeter of the triangle is:

`\begin{gathered} P=AB+BC+AC \\ P=12+5+13 \\ P=30 \end{gathered}`