Answer :
Given Data:
The area of the rectangle square is: A=80 square ft
The length of the floor is 2 feet less than the width of the flor.
[tex]l=w-2[/tex]Here, 'l' represents the length and 'w' represents the width.
The expression to calculate the area of a rectangle is,
[tex]\begin{gathered} A=l\times w \\ 80=l\times w \end{gathered}[/tex]Substitute 'l=w-2' in the above expression, and solve for 'w'.
[tex]\begin{gathered} 80=(w-2)\times w \\ 80=w^2-2w \\ w^2-2w-80=0 \end{gathered}[/tex]The above expression if a quadratic equation. The solution for the equation is,
[tex]\begin{gathered} w-10w+8w-80=0 \\ w(w+10)+8(w+10)=0 \\ (w-8)(w+10)=0 \\ w=8\text{ or -10} \end{gathered}[/tex]The value of w can not be -10 since it is a length.
Thus, the leidth of the rectangle is 10 ft.
Substitute the value of w in the expression of 'l'.
[tex]\begin{gathered} l=w-2 \\ l=10-2 \\ l=8 \end{gathered}[/tex]Thus, the length of the floor is 8 ft and the width of the floor is 10 ft.
