Answer:
The width and length of the rectangle are [tex]22[/tex] and [tex]16+x[/tex], for [tex]x > -16[/tex], respectively.
Step-by-step explanation:
From Geometry, we remember that area of the rectangle ([tex]A[/tex]) is defined by:
[tex]A = w\cdot l[/tex] (1)
Where:
[tex]w[/tex] - Width.
[tex]l[/tex] - Length.
In addition, we know that area is described by a first-order polynomial:
[tex]A = 352+22\cdot x[/tex] (2)
Meaning that is the product of another first-order polynomial and a constant. That is:
[tex]A = a\cdot (b+c\cdot x)[/tex] (3)
Now we determine the Great Common Divisor of 352 and 22:
[tex]352 = 2\times 2\times 2 \times 2 \times 2 \times 11[/tex]
[tex]22 = 2\times 11[/tex]
The Great Common Divisor is 22.
Then, the area of the rectangle can be expressed by this expression:
[tex]A = 22\cdot (16+x)[/tex] (3b)
According to this, the width and length of the rectangle are [tex]22[/tex] and [tex]16+x[/tex], for [tex]x > -16[/tex], respectively.
