Question

Connie want to create a tile mosaic to cover her rectangular patio table. The amount of tiles she will need to cover the table top can be represented by the expression 2r2 - 288. Which of the following could represent the dimensions of her table top? A. length =x+12,width=x-12B.length=2x+24,width=x-12C.length=x+12,width=2x-12D.length=2x+12,width=x+24

Answer 1

The area of a rectangle is:

Area = length x width

The area given is:

$2x^2-288$

We can factorize this expression and find the length and width. Shown below is the process:

$\begin{gathered} 2x^2-288 \\ =2(x^2-144) \\ =2(x+12)(x-12) \\ =(2(x)+2(12))(x-12) \\ =(2x+24)(x-12) \end{gathered}$

So,

Length would be "2x + 24"

Width would be "x - 12"

From the options, our answer is :

B