emmagracethomas05
Answered

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Find the perimeter of the triangle in units. Round to two decimal
places as necessary.

Find The Perimeter Of The Triangle In Units Round To Two Decimal Places As Necessary class=

Sagot :

mhanifa

Answer:

  • 54.56 units

Step-by-step explanation:

The vertices are:

  • K(-12,2), L(-7,12), J(3,-10)

Find the sides using distance formula:

  • KL = [tex]\sqrt{(-7+12)^2+(12-2)^2} = \sqrt{125}[/tex] ≈ 11.18
  • LJ = [tex]\sqrt{(3+7)^2+(-10-12)^2} = \sqrt{584}[/tex] ≈ 24.17
  • KJ = [tex]\sqrt{(3+12)^2+(-10-2)^2} = \sqrt{369}[/tex] ≈ 19.21

Find perimeter:

  • P = KL + LJ + KJ
  • P = 11.18 + 24.17 + 19.21 = 54.56 units
semsee45

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:

https://brainly.com/question/28144723

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