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.

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.