Question

An architect is designing a new library. 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.

Dimensions of the bookshelf space:
length = ( _ₓ + __ ) ft
width = ( _ₓ + __ ) ft

Area of the bookshelf space:
area = ( _ₓ² + _ₓ + __ ) ft²

a) (x + 3, x) / (x² + 3x + 6)
b) (x + 3, x + 8) / (x² + 11x + 24)
c) (x, x + 3) / (x² + 3x)
d) (x, x + 6) / (x² + 6x)

Answer 1

The dimensions of the bookshelf space are x + 3 ft by x ft. The area of the bookshelf space is (x + 3)(x) = x^2 + 3x ft².

Step-by-step explanation:

The dimensions of the bookshelf space can be expressed as x + 3 ft by x ft. The area of the bookshelf space can be calculated by multiplying the length and width of the space. Therefore, the area of the bookshelf space is (x + 3)(x) = x^2 + 3x ft².

Based on the options provided, the correct answer would be (x, x + 3) / (x² + 3x) ft².

Answer 2

The correct dimensions of the bookshelf space in the library are represented by (x + 3) ft for the length and (x + 8) ft for the width, making the area (x^2 + 11x + 24) ft^2.

Step-by-step explanation:

The dimensions of the bookshelf space in the library can be calculated by considering the width and length of each bookshelf, along with the spacing between them and the walkway. Each bookshelf is x feet wide and (x + 3) feet long, there are 3 feet of space between each bookshelf, and the walkway between the two rows of bookshelves is 2 feet wide. When visualizing the arrangement, there will be a bookshelf, then 3 feet of space, followed by the 2 feet walkway, then another 3 feet of space before the next bookshelf's width. Thus, the total width of the bookshelf space is '2x + 8' feet (x for one bookshelf, x for the other, and 8 feet for the spaces and walkway).

For the length, as each bookshelf is (x + 3) feet long, and there are no additional spaces mentioned, it is assumed that there are just two bookshelves side by side, making the total length simply 'x + 3' feet.

The area of the bookshelf space is then calculated by multiplying length and width, which gives us: 'area = (x + 3)(2x + 8) = 2x2 + 8x + 6x + 24 = 2x2 + 14x + 24' square feet.

The correct answer is thus option b) (x + 3, x + 8) / (x2 + 11x + 24), representing the length, width, and area of the bookshelf space, respectively.