Question

The rectangle has an area of 4(x+3) square units.

Answer 1

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 :)

Answer 2

Suppose there is a rectangle with a width and length of x and y. The area would be xy.

A rectangle with width and length 2x and 2y would have an area of 4xy.

In essence, when you multiply the lengths by 2, the area multiplies by 2 SQUARED.

4(4(x+3)) = 16(x+3).

The ratio will be the same for any value of x because the area is still being multiplied by the same 2².