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

2x + 2

Explanation:

`length \: of \: screen = (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}}`