Respuesta :
1) We were told to look for the dimension of the bookshelf space which are the Length and Width.
[tex]\begin{gathered} \text{Length of the bookshelf space=5}\times3ft+6(xft) \\ \text{Length}=15ft+6\text{xft}=3(5+2x)ft \end{gathered}[/tex]Since we have 5numbers of the 3ft and 6numbers of the bookshelf,
Therefore, the Length= 3(5+2x)ft.
[tex]\begin{gathered} \text{Width}=2(x+3)ft+2ft \\ =2xft+6ft+2ft=2\text{xft}+8ft=2(x+4)ft \\ \end{gathered}[/tex]Since the width of the bookshelf space consists of 2numbers of the bookshelf,
Therefore, the Width= 2(x+4)ft.
Therefore, the dimensions of the bookshelf space are given below:
Length=3(5+2x)ft
Width=2(x+4)ft.
2) Area of the bookshelf space= Length×width
[tex]\begin{gathered} \text{Area}=3(5+2x)\times2(x+4) \\ =(15+10x)(2x+8) \\ =15(2x+8)+10x(2x+8) \\ =30x+120+20x^2+80x \end{gathered}[/tex][tex]\begin{gathered} \text{Area}=20x^2+30x+80x+120 \\ =20x^2+110x+120 \end{gathered}[/tex]The area of the bookshelf space is 20x²+110x+120.
