hello
to solve the question presented here, we need to apply the formula of area and perimeter of a rectangle
height = 2 cm
volume = 50cm^3
length = 5 + 2x
width = x
volume = length * width * height
we can simply plug in the variables and get an equation
[tex]\begin{gathered} volume=length\times wi\differentialD tth\times height \\ 50=(5+2x)\times x\times2 \\ 50=2x(5+2x) \\ 50=10x+4x^2 \\ 4x^2+10x-50=0 \\ 2x^2+5x-25=0 \end{gathered}[/tex]since we have our quadratic equation, we can proceed to solve through using any of the methods
during the process of this session, i'll use formula method
[tex]\begin{gathered} 2x^2+5x-25=0 \\ a=2 \\ b=5 \\ c=-25 \\ x=-b\pm\frac{\sqrt{b^2-4ac}}{2a} \\ x=-5\pm\frac{\sqrt{5^2-4\cdot2\cdot(-25)}}{2\cdot2} \\ x=-5\pm\frac{\sqrt{25--200}}{4} \\ x=-5\pm\frac{\sqrt{25+200}}{4} \\ x=-5\pm\frac{15}{4} \\ x=\frac{-5+15}{4}\text{ or x = }\frac{-5-15}{4} \\ x=\frac{10}{4}\text{ or x = -5} \\ x=2.5\text{ or -5} \end{gathered}[/tex]but dimension can't be negative
x = 2.5
width = 2.5cm
length = 5+ 2*2.5 = 10cm
height = 2cm
