Answer: The correct option is (A) 2 ft by 6 ft.
Step-by-step explanation: Given that a table has an area of 12 ft squared and a perimeter of 16 ft.
We are to find the dimensions of the table.
Let l and b denote the length and breadth of the rectangular table, so we have
[tex]Area=12\\\\ \Rightarrow l\times b=12\\\\\Rightarrow l=\dfrac{12}{b}~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]Perimeter=16\\\\\Rightarrow 2(l+b)=16\\\\\Rightarrow l+b=8\\\\\Rightarrow \dfrac{12}{b}+b=8\\\\\Rightarrow b^2-8b+12=0\\\\\Rightarrow b^2-6b-2b+12=0\\\\\Rightarrow (b-2)(b-6)=0\\\\\Rightarrow b-2=0,~~~b-6=0\\\\\Rightarrow b=2,6.[/tex]
From equation (i), we get
[tex]l=\dfrac{12}{2}=6,\\\\l=\dfrac{12}{6}=2.[/tex]
Thus, the dimension of the table is 2 ft by 6 ft.
Option (A) is correct.
