The length of a rectangle is 3x+7 .the width is x-4 . express the area of the rectangle in terms of the variable x. a) 3x^2 -5x-28 b) 3x^2 +5x +28 c) 2x^2 +4 x-28 d ) 3x^2 -5x +28

A) 3x²-5x-28. The area of the rectangle  with length 3x+7 and width x-4 can be represented as 3x²-5x-28.

The equation to find the area of the rectangle is simply A = l * w. This means that the area of a rectangle is equal to the product of its length (l) by its width (w), or of its length by its width.

A = w*l

A = (3x + 7)(x -4) = (3x)(x) + (3x)(-4) + (7)(x) + (7)(-4)

A = 3x² - 12x + 7x - 28

A = 3x² -5x - 28

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