Answer:
x represents the width of the bookcase.
Step-by-step 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
[tex]2w+2w+2(w+2)=4w+2(w+2)[/tex] ...(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
[tex]4x+2(x+2)[/tex] ...(ii)
From (i) and (ii) we get
[tex]x=w[/tex]
Therefore, x represents the width of the bookcase.
