The total area of a rectangular-shaped garden is:
[tex]x^3+7x^2+7x-15[/tex]We have that the area of a rectangle is
[tex]A=L\cdot W[/tex]We have the total area given by the expression above. We also have the length, given by:
[tex]L=x+3[/tex]Then
[tex]x^3+7x^2_{}+7x-15=(x+3)\cdot W[/tex][tex]W=\frac{x^3+7x^2+7x-15}{x+3}[/tex]We need to solve this polynomial division:
Therefore, the width is
[tex]x^2+4x-5[/tex]The perimeter is the sum of all the sides of the rectangle:
[tex]2W+2L\rightarrow2\cdot(x^2+4x-5)+2\cdot(x+3)=(2x^2+8x-10)+2x+6[/tex][tex]2x^2+10x-4[/tex]So, the perimeter is 2x^2+10x-4.
The width is x^2+4x-5.
