Respuesta :
Consider the vertices of parallelogram JKLM with vertices J(2,2) , K(5,3) , L(5,-3) and M(2,-4).
Perimeter JKLM = Length JK + Length KL + Length LM + Length JM
Length JK = (2,2) (5,3)
The length(or distance) between two points say [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given by the distance formula:
[tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
Now, length JK = [tex]\sqrt{(5-2)^{2}+(3-2)^{2}}[/tex]
= [tex]\sqrt(10)[/tex] units
Since, JKLM is a parallelogram. In parallelogram opposite sides are equal in length.
Therefore, LM = [tex]\sqrt(10)[/tex] units
Now, length KL = [tex]\sqrt{(5-5)^{2}+(-3-3)^{2}}[/tex]
= 6 units
Since, JKLM is a parallelogram. In parallelogram opposite sides are equal in length.
Therefore, JM = 6 units
Perimeter of JKLM = [tex]\sqrt(10)[/tex] + [tex]\sqrt(10)[/tex] + 6 + 6
= 2 [tex]\sqrt(10)[/tex] + 12
= 18.324
Rounding to the nearest tenth, we get
= 18.3 units.
Therefore, the perimeter of JKLM is 18.3 units.
