Question

felix has a bookcase that is 2 feet taller than it is wide the expression 4x+2 (x+2)represents the total length of a board that can be cut for the top bottom 2 shelves and 2 sides of the bookcase what does x represent in this expression

Answer 1

x represents the width of the bookcase.

Explanation:

Let w be the width of the bookcase.

Bookcase that is 2 feet taller than it is width.

Length = w+2 feet.

Length of a board that can be cut for the top bottom 2 shelves and 2 sides of the bookcase.

Top and bottom = w+w = 2w

2 shelves = w+w = 2w

2 sides of the bookcase = 2(w+2)

Total length of a board that can be cut for the top bottom 2 shelves and 2 sides of the bookcase is

`2w+2w+2(w+2)=4w+2(w+2)` ...(i)

It is given that total length of a board that can be cut for the top bottom 2 shelves and 2 sides of the bookcase is

`4x+2(x+2)` ...(ii)

From (i) and (ii) we get

`x=w`

Therefore, x represents the width of the bookcase.