Question

The area of a rectangular computer screen is 4x2+ 20x+16. The width of the screen is 2x+ 8. What is the length of the screen?

Answer 1

Answer:

2x + 2

Step-by-step explanation:

$length \: of \: screen = \frac{area}{width} \\ \\ = \frac{4 {x}^{2} + 20x + 16}{2x + 8} \\ \\ = \frac{4( {x}^{2} + 5x + 4)}{2(x + 4)} \\ \\ = \frac{2( {x}^{2} + 4x + x+ 4)}{(x + 4)} \\ \\ = \frac{2 \{x( {x} + 4) +1( x+ 4) \}}{(x + 4)} \\ \\ = \frac{2 ( {x} + 4) ( x+ 1) }{(x + 4)} \\ =2 (x + 1) \\ \purple{ \bold{length \: of \: screen = 2x + 2}}$