Marvin wants to purchase a rectangular rug. It has an area represented by the expression 4x^2+64x+256. what is the length and wi

Length = x + 8

Width = x + 8

Explanation:

Provided:

4x² + 64x + 256 = 0

Dividing by 4 gives us:

x² + 16x + 64 = 0

x² + 8x + 8x + 64 = 0

x(x + 8) + 8 (x + 8) = 0

(x + 8)(x + 8) = 0

Length = x + 8

Width = x + 8

The rectangle’s area is derived from length multiplied by width. Thus, the factors represent length and width.

Additionally, the factors found in the factored forms signify the rectangle's length and width.

Detailed explanation:

Here we have Marvin who intends to buy a rectangular rug. The area is expressed as 4x^2 + 64x + 256. We need to determine the dimensions. Also, we should clarify what the factors in the expressed form signify. Let's analyze:

The area expression is , Let’s factor this

⇒

⇒

⇒

⇒

Knowing that the area of a rectangle equals , we can compare it to the above equation and derive:

Additionally, the factors in the factored forms signify the rectangle's length and width.