Answer:
The perimeter of the rectangle EFGH is 17.09
Step-by-step explanation:
Firstly, we have to calculate the height and width of the rectangle EFGH.
For it, let determine the vectors corresponding to each dimension.
Let [tex]V_G_H[/tex] the width vector:
[tex]V_G_H=(-3-2,4-2)=(-5,2)[/tex]
Let [tex]V_H_E[/tex] the height vector:
[tex]V_H_E=(2-1,2-(-1))=(1,3)[/tex]
Then, let determine the modulus of each vector.
[tex]|V_G_H|=\sqrt{(-5)^2+2^2} =\sqrt{29}[/tex]
[tex]|V_H_E|=\sqrt{1^2+3^2} =\sqrt{10}[/tex]
The modulus represents the length of each dimension.
Finally, the perimeter of a rectangle is:
[tex]Perimeter EFGH=2*|V_G_H|+2*|V_H_E|=2*\sqrt{29} +2*\sqrt{10} \\Perimeter EFGH=17.09[/tex]
