Answer:
[tex]x=-2\pm2\sqrt13[/tex]
Step-by-step explanation:
The area of the triangle is;
[tex]A=\frac{1}{2} \times b\times h[/tex]
[tex]b=x+4[/tex]
[tex]h=x[/tex]
[tex]Area=A=24[/tex]
[tex]A=\frac{1}{2}\times[(x+4)\times x] \\24=\frac{x^{2} +4x}{2} \\24\times2=x^{2} +4x\\48=x^{2} +4x\\x^{2} +4x-48=0\\[/tex]
This can only be solved by the quadratic formula.
[tex]x=\frac{-b\pm\sqrt {b^{2}-4ac }}{2a}[/tex]
where;
[tex]a=1\\b=4\\c=-48[/tex]
and we get,
[tex]x=-2\pm2\sqrt13[/tex]
