Step-by-step explanation:
Three coordinates of triange are given to us and we need to find its perimeter . We know that perimeter is the sum of all sides . Lets find the distance between each sides using distance formula .
• Distance between A and B :-
[tex]\tt\to D_{(AB)} =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\tt\to D_{(AB)} =\sqrt{(3-2)^2+(4-4)^2}\\\\\tt\to D_{(AB)} =\sqrt{( 1^2+0^2 )} \\\\\tt\to D_{(AB)} =\sqrt{1} \\\\\tt\to \boxed{\orange{\tt D_{(AB)} = 1\ units }}[/tex]
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• Distance between A and C :-
[tex]\tt\to D_{(AC)} =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\tt\to D_{(AC)} =\sqrt{(3-2)^2+(4+4)^2}\\\\\tt\to D_{(AC)} =\sqrt{( 1^2+8^2 )} \\\\\tt\to D_{(AC)} =\sqrt{65} \\\\\tt\to \boxed{\orange{\tt D_{(AC)} = \sqrt{65}\ units }}[/tex]
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• Distance between C and B :-
[tex]\tt\to D_{(CB)} =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\tt\to D_{(CB)} =\sqrt{(3-3)^2+(4+4)^2}\\\\\tt\to D_{(CB)} =\sqrt{( 8^2+0^2 )} \\\\\tt\to D_{(CB)} =\sqrt{65} \\\\\tt\to \boxed{\orange{\tt D_{(CB)} = \sqrt{65}\ units }}[/tex]
Hence the total perimeter will be ,
[tex]\to\tt D_{(AB)}+D_{(BC)}+D_{(CA)}\\\\\tt\to \sqrt{65}+\sqrt{65}+1 \\\\\tt\large\to\underline{\boxed{\green{\tt 1 +2\sqrt{65} \:\:units }}}[/tex]
