Question

Use Structure The area of a rectangular

Answer 1

Answer:

The width and length of the rectangle are $22$ and $16+x$, for $x > -16$, respectively.

Step-by-step explanation:

From Geometry, we remember that area of the rectangle ($A$) is defined by:

$A = w\cdot l$ (1)

Where:

$w$ - Width.

$l$ - Length.

In addition, we know that area is described by a first-order polynomial:

$A = 352+22\cdot x$ (2)

Meaning that is the product of another first-order polynomial and a constant. That is:

$A = a\cdot (b+c\cdot x)$  (3)

Now we determine the Great Common Divisor of 352 and 22:

$352 = 2\times 2\times 2 \times 2 \times 2 \times 11$

$22 = 2\times 11$

The Great Common Divisor is 22.

Then, the area of the rectangle can be expressed by this expression:

$A = 22\cdot (16+x)$ (3b)

According to this, the width and length of the rectangle are $22$ and $16+x$, for $x > -16$, respectively.