The correct answer is:
2√2 + 2√5
Explanation:
To find the perimeter, we need the length of each side of the kite. To find this, we find the distance between each vertex.
To find the distance from M to N:
[tex] d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}
\\
\\=\sqrt{(4-3)^2+(3-2)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt{2} [/tex]
To find the distance from N to K:
[tex] d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}
\\
\\=\sqrt{(3-4)^2+(5-3)^2}=\sqrt{(-1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5} [/tex]
To find the distance from K to L:
[tex] d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}
\\
\\=\sqrt{(2-3)^2+(3-5)^2}=\sqrt{(-1)^2+(-2)^2}=\sqrt{1+4}=\sqrt{5} [/tex]
To find the distance from L to M:
[tex] d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}
\\
\\=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{1^2+(-1)^2}=\sqrt{1+1}=\sqrt{2} [/tex]
To find the perimeter, we add together all of the side lengths:
√2+√5+√5+√2
Treating the radicals as like terms, we have:
2√2+2√5
