By definition, the perimeter of a rectangle is given by:
[tex] P = 2w + 2l
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Where,
w: width of the rectangle
l: length of the rectangle
To find the width and length, we use the formula of distance between points:
[tex] d = \sqrt{(x2-x1) ^ 2 + (y2-y1) ^ 2}
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For the width we have:
[tex] w = \sqrt{(- 3 - (- 4)) ^ 2 + (4-1) ^ 2}
w = \sqrt{10}
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For the long we have:
[tex] l = \sqrt{(- 3-2) ^ 2 + (4-2) ^ 2}
l =\sqrt{29}
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Then, replacing values we have:
[tex] P = 2\sqrt{10} + 2\sqrt{29}
[/tex]
Answer:
the perimeter of rectangle EFGH is:
[tex] P = 2\sqrt{10} + 2\sqrt{29}
[/tex]
