If rectangle abcd is dilated by a scale factor of 3 with a center of dilation at vertex d, what is the perimeter of a'b'c'd'?

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.

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