[tex]Answer: \\The\: width\: is \: 6 \: {in}^{2} \\ \\ Step\: by\: step\: explanation: \\ Let \: x \: be \: the \: width \: of \: the \: rectangle,\: x > 0\Rightarrow the \: length:2x + 8 \\ We \: have \: an \: equation:x(2x + 8) = 120 \\ \Leftrightarrow 2 {x}^{2} + 8x + 8= 128 \\ \Leftrightarrow {x}^{2} + 4x + 4 = 64 \\ \Leftrightarrow {(x + 2)}^{2} = 64 \\ \Leftrightarrow x + 2 = \pm8 \\ \Leftrightarrow x = 6 \: \vee \: x = - 10 \\ \Rightarrow x = 6 \: (x > 0)[/tex]
