Question

An architect is designing a new library. As shown, the library’s floor plan is a rectangle divided into a bookshelf space with bookshelves, and a reading space with a rug and chairs. Each bookshelf is x ft wide and x + 3 ft long. The bookshelves are 3 ft from each other. The walkway between the two rows of bookshelves is 2 ft wide.

Answer 1

1) We were told to look for the dimension of the bookshelf space which are the Length and Width.

`\begin{gathered} \text{Length of the bookshelf space=5}*3ft+6(xft) \\ \text{Length}=15ft+6\text{xft}=3(5+2x)ft \end{gathered}`

Since we have 5numbers of the 3ft and 6numbers of the bookshelf,

Therefore, the Length= 3(5+2x)ft.

`\begin{gathered} \text{Width}=2(x+3)ft+2ft \\ =2xft+6ft+2ft=2\text{xft}+8ft=2(x+4)ft \\ \end{gathered}`

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

`\begin{gathered} \text{Area}=3(5+2x)*2(x+4) \\ =(15+10x)(2x+8) \\ =15(2x+8)+10x(2x+8) \\ =30x+120+20x^2+80x \end{gathered}`
`\begin{gathered} \text{Area}=20x^2+30x+80x+120 \\ =20x^2+110x+120 \end{gathered}`

The area of the bookshelf space is 20x²+110x+120.