Respuesta :
Answer:
The perimeter of the rectangle A'B'C'D' = 6 times the perimeter of rectangle ABCD.
Step-by-step explanation:
If a rectangle ABCD is dilated by a scale factor of 3 with a center of dilation at vertex D, then D = 3D'
Therefore, the length and width of the dilated rectangle A'B'C'D' by the scale factor of 3.
Therefore, A'B'= 3 AB and A'D'= 3 AD
Perimeter of the rectangle ABCD = 2(length + width)
= 2(AB + AD)
Perimeter of the rectangle A'B'C'D' = 2(A'B' + A'D')
Now plug in A'B' = 3 AB and A'D' = 3 AD
Perimeter of of the rectangle A'B'C'D' = 2(3 AB + 3 AD) = 2(3)(AB + AD)
Perimeter of the rectangle A'B'C'D' = 6( AB + AD)
So, the perimeter of the rectangle A'B'C'D' = 6 times the perimeter of rectangle ABCD.
Therefore, the answer is the perimeter of the rectangle A'B'C'D' = 6 times the perimeter of rectangle ABCD.
