WILL MARK BRAINLEST Karen is adding a border to a rectangular poster. The border will have a uniform width of x inches and run along all four sides, so Karen uses the functions l and w to model the length and width, in inches, of her poster after she adds the border.
l(x) = 2x + 18
w(x) = 2x + 24

Which function correctly represents the total area, in square inches, of Karen’s poster, when a border x inches wide is included in the area?

A. A(x) = 4x2 + 42x + 432
B. A(x) = 4x + 432
C. A(x) = 4x2 + 84x + 432
D. A(x) = 4x2 + 432

C

Step-by-step explanation:

(2x + 18)(2x + 24) = Total area = A(x)

A(x) =

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have