Question

Use Structure The area of a rectangular

playground has been extended on one side.

The total area of the playground, in square

meters, can be written as 352 +22x.

Rewrite the expression to give a possible set

of dimensions for the playground,

Answer 1

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

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* 2* 2 * 2 * 2 * 11`

`22 = 2* 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.