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?
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I think it's 5
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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inter is correct
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)
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.