Question

Marvin wants to purchase a rectangular rug. It has an area represented by the expression 4x^2+64x+256. what is the length and width. also what do the factors in the factored expressions represent

Answer 1

$Length = 2x+16\\Breadth=2x+16$

And , factors in the factored expressions represents length and width of rectangle .

Step-by-step explanation:

Here we have , Marvin wants to purchase a rectangular rug. It has an area represented by the expression 4x^2+64x+256. what is the length and width. We need to find what is the length and width. also what do the factors in the factored expressions represent . Let's find out:

We have expression of area as $4x^2+64x+256$  , Let's factorize this

⇒ $4x^2+64x+256$

⇒ $4x^2+32x+32x+256$

⇒ $2x(2x+16)+16(2x+16)$

⇒ $(2x+16)(2x+16)$

We know that area of rectangle = $length(breadth)$ , comparing this to above equation we get:

$Length = 2x+16\\Breadth=2x+16$

And , factors in the factored expressions represents length and width of rectangle .

Answer 2

Length = x + 8

Width = x + 8

Explanation:

Given:

4x² + 64x + 256 = 0

Dividing the equation by 4 we get:

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 area of the rectangle is length X width. So, the factors of the equation represents length and width.