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Sean is creating a series of rectangles, one inside the other. The length of the first rectangle, Rectangle A, is four inches. Sean dilates Rectangle A about its center by a scale factor of two to get Rectangle B. He repeats this process using the same scale factor till he gets a rectangle of length 32 inches. How many dilations did Sean perform including the dilation of Rectangle A?
a to b gives length of 8. Next, 8 to 16 then 16 to 32. so he did it 3 times
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If you want a formula, you can actually use the geometric progression for this. Anought = 4 inches. Geometric ratio = 2 A sub n = 32 inches. n is the unknown. The solution for geo series is Asubn = (Anought)((geo ratio)^(n-1)) Substituting, we have: 32 = (4)((2)^(n-1)) 8 = 2^(n-1) 2^3 = 2^(n-1) 3=n-1 n=4 He did 4 dilations.
He did 3 dilations, i'm sorry. 32 inches was the length of his 4th rectangle. But the dilations didn't start from n=1 as this is the original rectangle, there weren't dilations performed.