Option A
The quadratic equation can be used to determine the thickness of the border, x is [tex]4 x^{2}+156 x-2484=0[/tex]
Solution:
Given, Lisa wants to build a table and put a border around it.
The table and border must have an area of 3,996 square inches.
The table is 42 inches wide and 36 inches long without the border.
To find the quadratic equation used to determine the thickness of the border:
So, area of table and border = 3996
Area = (length + 2x)(width + 2x)
Here “2x” represents the border around table
[tex]\begin{array}{l}{\rightarrow(36+2 x)(42+2 x)=3996} \\\\ {\rightarrow 42 \times 36+84 x+4 x^{2}+72 x=3996} \\\\ {\rightarrow 4 x^{2}+156 x=3996-42 \times 36} \\\\ {\rightarrow 4 x^{2}+156 x=3996-1512} \\\\ {\rightarrow 4 x^{2}+156 x=2484} \\\\{\rightarrow 4 x^{2}+156 x-2484=0}\end{array}[/tex]
Hence, the equation is [tex]4 x^{2}+156 x-2484=0[/tex] so option A is correct
