The rectangle has an area of 4(x+3) square units.
a- if the dimensions of the rectangle are doubled, what is the area of the new rectangle in terms of x? show your work.
b- will the ratio of the area of the original rectangle to the area of the larger rectangle be the same for any positive value of x? explain.

A)
If it has an area of 4(x+3) we can think that one side has a length of 4, and the other has a length of (x+3).

So, if the dimensions were doubled, 4 x 2 = 8. And 2(x+3) = 2x+6.

The new area would be:

8(2x+6) = 16x+48.

B) 
The ratio will be the same. For example lets plug in some points:

x=0
4(0+3) = 4(3) = 12

And 
16(0)+48 = 0+48 = 48

So the ratio is 48/12 = 4

Lets plug in another point.

x=2
4(2+3)= 4(5) = 20

And
x=2
16(2)+48 = 32 + 48 = 80

80/20 = 4

So the ratio is the same :)

This is what i found “answer: a rigid transformation preserves both the side lengths and the angle measures of a polygon. step-by-step explanation: rigid transformations are the transformations which does not affect the size and the shape of figure .” i hope this you for what your looking for. can you plz mark me brainliest?