Question

Consider the triangle below.

Answer 1

Answer:

Option A is correct.

Step-by-step explanation:

$\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

Using the above mentioned distance formula, we have:

$\mathrm{Distance\:between\:}\left(1,\:3\right)\mathrm{\:and\:}\left(3,\:-2\right):\quad \sqrt{29}\:\:\:\mathrm{or}\:\:5.39\:\\\\\\\mathrm{Distance\:between\:}\left(1,\:3\right)\mathrm{\:and\:}\left(-4,\:-1\right):\quad \sqrt{41}\:\:\:\mathrm{or}\:\:6.4\:\\\\\\\mathrm{Distance\:between\:}\left(3,\:-2\right)\mathrm{\:and\:}\left(-4,\:-1\right):\quad 5\sqrt{2}\:\:\:\mathrm{or}\:\:7.07\:$

Add the length of three sides of triangles, we have:

Perimeter = 5.39+6.4+7.07 = 18.86