we are given that
Base=3x+6
Height=x+4
[tex] \\
\
A=\frac{1}{2}bh\\
\\
120=\frac{1}{2}(3x+6)(x+4)\\
\\
240=(3x+4)(x+4)\\
\\
\
3x^2+12x+4x+16=240\\
\\
\
3x^2+16x-224=0\\
\\
x=\frac{-16+\sqrt{16^2-4\cdot \:3\left(-224\right)}}{2\cdot \:3},x=\frac{-16-\sqrt{16^2-4\cdot \:3\left(-224\right)}}{2\cdot \:3}\\
\\
x=\frac{4\left(\sqrt{46}-2\right)}{3},\:x=-\frac{4\left(2+\sqrt{46}\right)}{3}\\
\\
\
x=6.376\\ [/tex]
as we can take only positive values.
Base=3*6.376+6=25.128
Height=6.376+4=10.376
