Question

What is the perimeter of the triangle? Round to the nearest tenth.

Answer 1

Answer: 19.8 Units

Step-by-step explanation:

The triangle is shown in the attached figure, and have three vertices: $AB$, $AC$ and $BC$.

Each vertice represents a point in the cartesian plane and the length of each side of the triangle is the modulus of each vector.

In this sense, the modulus $m$ is calculated as shown:

$m=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$

Hence, for each vector:

$AB=\sqrt{(-2-3)^{2} + (3-0)^{2}}=\sqrt{34}$

$AC=\sqrt{(-2-(4))^{2} + (3-(-3))^{2}}=\sqrt{40}$

$BC=\sqrt{(-4-3)^{2} + (-3-0)^{2}}=\sqrt{58}$

Now, the perimeter of a triangle is the sum of its three sides:

$AB+AC+BC=\sqrt{34} + \sqrt{40} + \sqrt{58}$

Finally:

$AB+AC+BC=19.77 \approx 19.8$