Perimeter is the sum of all the sides of a shape.

|LM| = $\sqrt{{\mathrm{(3\; -\; 2)}}^2+{\mathrm{(5\; -\; -1)}}^2}$

Notes:
1. -- = +
2. 5 - -1 = 5 + 1 = 6

|LM| = $\sqrt{1^2+6^2}$

|LM| = $\sqrt{\mathrm{1\; +\; 36}}$

|LM| = $\sqrt{37}$ = 6.08 units

|MN| = $\sqrt{{\mathrm{(3\; -\; -1)}}^2+{\mathrm{(5\; -\; 6)}}^2}$

Notes:
1. -- = +
2. 3 - -1 = 3 + 1 = 4

|MN| = $\sqrt{4^2+{\mathrm{(-1)}}^2}$

|MN| = $\sqrt{\mathrm{16\; +\; 1}}$

|MN| = $\sqrt{17}$ = 4.12 units

|LN| = $\sqrt{{\mathrm{(2\; -\; -1)}}^2+{\mathrm{(-1\; -\; 6)}}^2}$

Notes:
1. -- = +
2. 2 - -1 = 2 + 1 = 3

|LN| = $\sqrt{3^2+{\mathrm{(-7)}}^2}$

|LN| = $\sqrt{\mathrm{9\; +\; 49}}$

|LN| = $\sqrt{58}$ = 7.62 units

Perimeter of ∆LMN = |LM| + |MN| + |LN|

Perimeter of ∆LMN = 6.08 units + 4.12 units + 7.62 units

Perimeter of ∆LMN = 17.82 units ≈ 17.8 units(one decimal place)