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Polygon ABCD has a perimeter of 40. Its dilation has a scale factor of 3. What would the perimeter be for the enlargement image of A'B'C'D'?

Respuesta :

Answer:

120

Step-by-step explanation:

If the dilation has a scale factor of 3, it means that each side of the polygon ABCD increased to 3 times the original length.

So, if the perimeter is the sum of the sides, we have:

[tex]P = AB + BC + CD + DA = 40[/tex]

[tex]P' = 3AB + 3BC + 3CD + 3DA[/tex]

[tex]P' = 3(AB + BC + CD + DA)[/tex]

[tex]P' = 3P = 120[/tex]

So the perimeter is also 3 times higher, with a length of 120.

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