Answer: [tex]2\sqrt{37}+2\sqrt{29}+8\sqrt{2}\ \text{units}[/tex]
Step-by-step explanation:
Given
The coordinates of the triangle are [tex]K(-6,-2),L(6,-4),M(2,6)[/tex]
Distance between the two points is given by the distance formula
[tex]d=\sqrt{\left( x_2-x_1\right)^2+\left( y_2-y_1\right)^2}[/tex]
Distance between K and L
[tex]KL=\sqrt{\left( 6+6\right)^2+\left( -4+2\right)^2}\\KL=\sqrt{\left( 12\right)^2+\left( -2\right)^2}\\KL=\sqrt{144+4}\\KL=\sqrt{148}\ \text{units}[/tex]
For L and M
[tex]LM=\sqrt{\left( 2-6\right)^2+\left( 6+4\right)^2}\\LM=\sqrt{\left( -4\right)^2+\left( 10\right)^2}\\LM=\sqrt{16+100}\\LM=\sqrt{116}[/tex]
For K and M
[tex]KM=\sqrt{\left( 8\right)^2+\left( 8\right)^2}\\KM=\sqrt{64+64}\\KM=8\sqrt{2}\ \text{units}[/tex]
The perimeter of the triangle is
[tex]\Rightarrow \sqrt{148}+\sqrt{116}+8\sqrt{2}\\\\\Rightarrow 2\sqrt{37}+2\sqrt{29}+8\sqrt{2}\ \text{units}[/tex]
