In the first series, the summation applies to the whole (2n+3) inside
the parentheses, so the 3 gets summed up 5 times.
But in the second one, the summation only applies to the 2n , so
the 3 is only added after the summation is finished.
The difference between five 3s the first time and one 3 the second time
is your 12 .
I found width=13.72 ft and length=43.72 ft.
Call one dimension of the rectangle x, the other will be x+30
You want an area A=600 ft^2 but A=length x width=x*(x+30)=600
Rearranging you get:

solving this quadratic equation you get a negative solution and a positive one that gives your result.
When the dilation is about the origin, the scale factor multiplies every coordinate. That is (considering the x-coordinate) ...
6·k = 3
k = 3/6 = 1/2
The appropriate choice is
1. 1/2
One half of something plus another half of something is equal to the thing
1/2x +1/2x = x
The reduced answer would be ?/10
The Method is that you add 1 block horizontally to the 2nd row of the figure every time you make a new one.