Answer
Find out the perimeter of △LMN .
To prove
Formula
[tex]Distance\ formula = \sqrt{{(x_{2} - x_{1})^{2} +{(y_{2} - y_{1})^{2} }[/tex]
Two points be L(2, 4) and M (-2,1)
Put in the formula
[tex]Distance\ formula = \sqrt{{(-2-2)^{2} +{(1-4)^{2} }[/tex]
Solving the above
[tex]Distance\ formula = \sqrt{{(-4)^{2} +{(-3)^{2} }[/tex]
[tex]LM = \sqrt{16+9}[/tex]
[tex]LM= \sqrt{25}[/tex]
[tex]\sqrt{25} = 5 unit[/tex]
Two points be M (-2,1) and N (-1,4)
[tex]Distance\ formula = \sqrt{{(-1+2)^{2} +{(4-1)^{2} }[/tex]
Solving the above
[tex]Distance\ formula = \sqrt{{(1)^{2} +{(3)^{2} }[/tex]
[tex]MN= \sqrt{1+9}[/tex]
[tex]MN = \sqrt{10\units}[/tex]
Two points be N (-1,4) and L (2,4)
[tex]Distance\ formula = \sqrt{{(2+1)^{2} +{(4-4)^{2} }[/tex]
Solving the above
[tex]NL = \sqrt{{(3)^{2} +{(0)^{2} }[/tex]
[tex]NL = \sqrt{9}[/tex]
[tex]\sqrt{9} = 3[/tex]
NL = 3 units
Perimeter of a △LMN = LM + MN +NL
[tex]Perimeter = 5 + \sqrt{10} + 3\\ Perimeter = 8 +\sqrt{10}\ units[/tex]
Option (d) is correct .
