What is the perimeter of △LMN?

Solution:

Given, the coordinates of the triangle are L(2, 4), M(-2, 1) and N(-1, 4).

We have to find the perimeter of the triangle LMN.

The length of each side of the triangle can be computed using distance formula,

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

Distance between LM = \(\sqrt{(-2-1))^{2}+(4-1)^{2}}\)

\(=\sqrt{(4)^{2}+(3)^{2}}\\=\sqrt{16+9}\\=\sqrt{25}\)

LM = 5 units

Distance between MN = \(=\sqrt{(-1-(-2))^{2}+(4-1)^{2}}

=\sqrt{(-1+2)^{2}+(3)^{2}}\\=\sqrt{1+9\\=\sqrt{10} }\)

MN = √10 units

Distance between NL = \(=\sqrt{(-2-(-1))^{2}+(4-4)^{2}}

=\sqrt{(2+1)^{2}+0}\\=\sqrt{(3)^{2} }\)

= √9

NL = 3 units

Perimeter = sum of length of each side of the triangle

Perimeter = LM + MN + NL

Perimeter = 5 + √10 + 3

Perimeter = 8 + √10 units.

Therefore, the perimeter of the triangle LMN is 8 + √10 units.

Summary:

The perimeter of the triangle LMN is 8 + √10 units.