[tex]Answer: \\ Let\: x\: be \: the \: base\Rightarrow the \: height:x - 4 \\ We \: have \: an \: equation: \frac{x(x - 4)}{2} = 48 \\ \Leftrightarrow {x}^{2} - 4x = 96 \\ \Leftrightarrow {x}^{2} - 4x + 4 = 100 \\ \Leftrightarrow {(x - 2)}^{2} = 100 \\ \Leftrightarrow x - 2 = 10 \: \vee \: x - 2 = - 10 \\ \Leftrightarrow x = 12\: \vee \:x = - 8 \\ \Rightarrow x = 12 \: (x \: can't \: be \: negative) \\ \Rightarrow Length \: of \: the \: base:12 \: m[/tex]
