A homeowner wants to enlarge a rectangular closet that has an area of (x2 + 9x + 20) ft?.

The length is (x + 5) ft. After construction, the area will be (x2 + 14x + 48) ft? with a length

of (x + 6) ft.

Part 1 out of 3

Find the dimensions of the closet before construction.

The dimension of the rectangular closet before construction =   (x + 5) ft by (x +  4) ft

Step-by-step explanation:

The homeowner has a rectangular closet and the area of the closet is (x² + 9x + 20) ft². The area of a rectangle is the length multiplied by the width.  The length is given as (x + 5) ft. After construction the area change to (x² + 14x + 48) ft². The length became (x + 6) ft.

The dimensions before construction can be calculated as follows:

Mathematically,

area of rectangle = Length × width

area = (x² + 9x + 20) ft².

Length =  (x + 5) ft

Width = unknown

area = LW

(x² + 9x + 20)  =  (x + 5) W

W = (x² + 9x + 20) / x + 5

W = (x +  4) ft

The dimension of the rectangular closet before construction =   (x + 5) ft by (x +  4) ft

width: (x+4) ft, length: (x+5) ft

Step-by-step explanation:

If the area was x2 + 9x + 20, and the length was (x+5), we find the width dividing the first polynomial by the second (or find what polynomial, multiplied by the second, will give us the first). We can see that the last value of the first polynomial is 20, and the last of the second is 5, so dividing these two values will give us the last value of the width polynomial, so we have that the width before construction is (x+4) ft.

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