The given expression is
[tex]16x^2+56x+24=0[/tex]
To determine the dimensions of the length and the height, we have to factor the expression.
We know that a = 16, b = 56, and c = 24. Remember that a is the coefficient of the quadratic variable, b is the coefficient of the linear variable, and c is the independent term.
Now, we use the quadratic formula
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
Let's replace all the values
[tex]\begin{gathered} x_{1,2}=\frac{-56\pm\sqrt[]{56^2-4\cdot16\cdot24}}{2\cdot16} \\ x_{1,2}=\frac{-56\pm\sqrt[]{3136-1536}}{32}=\frac{-56\pm\sqrt[]{1600}}{32} \\ x_{1,2}=\frac{-56\pm40}{32} \end{gathered}[/tex]
We have two solutions here
[tex]\begin{gathered} x_1=\frac{-56+40}{32}=\frac{-16}{32}=-\frac{1}{2} \\ x_2=\frac{-56-40}{32}=\frac{-96}{32}=-3 \end{gathered}[/tex]
If we express them as factors, it would be
[tex](2x+1)(x+3)[/tex]Which is equivalent to A.
