Respuesta :
Given:
The area of a rectangles
[tex]x^2-2x-3[/tex]And one of the adjacent sides has length is,
[tex](x+1)[/tex]Required:
To find the other side, and find an expression for the perimeter of the rectangle in simplest form.
Explanation:
[tex]A=L\times W[/tex][tex]\begin{gathered} x^2-2x-3=(x+1)\times W \\ \\ W=\frac{x^2-2x-3}{x+1} \end{gathered}[/tex][tex]\begin{gathered} \text{ x-3} \\ x+1)x^2-2x-3 \\ \text{ x}^2+x \\ =-3x-3 \\ -3x-3 \\ =0 \end{gathered}[/tex]Therefore, the other side is
[tex](x-3)[/tex]The perimeter of a rectangle is,
[tex]\begin{gathered} P=2A \\ \\ =2(x^2-2x-3) \\ \\ =2x^2-4x-6 \end{gathered}[/tex]Final Answer:
The other side of the rectangle is,
[tex](x-3)[/tex]The perimeter is,
[tex]2x^2-4x-6[/tex]