Answer:
54.56 units (2 d.p.)
Step-by-step explanation:
The perimeter of a two-dimensional shape is the sum of the lengths of its sides.
From inspection of the given diagram, the vertices of the triangle are:
- J = (3, -10)
- K = (-12, 2)
- L = (-7, 12)
To find the lengths of each side, use the distance between two points formula.
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]
Therefore:
[tex]\implies JK = \sqrt{(x_K-x_J)^2+(y_K-y_J)^2}[/tex]
[tex]\implies JK = \sqrt{(-12-3)^2+(2-(-10))^2}[/tex]
[tex]\implies JK = \sqrt{369}[/tex]
[tex]\implies KL = \sqrt{(x_L-x_K)^2+(y_L-y_K)^2}[/tex]
[tex]\implies KL = \sqrt{(-7-(-12))^2+(12-2)^2}[/tex]
[tex]\implies KL=\sqrt{125}[/tex]
[tex]\implies LJ = \sqrt{(x_J-x_L)^2+(y_J-y_L)^2}[/tex]
[tex]\implies LJ = \sqrt{(3-(-7))^2+(-10-12)^2}[/tex]
[tex]\implies LJ=\sqrt{584}[/tex]
Therefore:
[tex]\begin{aligned}\implies \sf Perimeter & = \sf JK + KL + LJ\\& = \sqrt{369}+\sqrt{125}+\sqrt{584}\\& = 54.55580455...\\& = 54.56\:\: \sf units\:(2\:d.p.)\end{aligned}[/tex]
Learn more about the distance formula here:
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