Answer:
[tex]x-\frac{1}{2}[/tex]
Step-by-step explanation:
The area of the rectangular window is equal to the product between the length of the window and its width:
[tex]A=L\cdot W[/tex] (1)
where
A is the area
L is the length
W is the width
In this problem, the area of the glass window is
[tex]A=2x^2+5x-12[/tex]
This can be rewritten as
[tex]A=(x+4)(x-\frac{1}{2})[/tex] (2)
The two expressions, in fact, are equivalent.
Also, we know that the width is
[tex]W=x+4[/tex] (3)
By comparing (1) with (2) and (3), we notice immediately that
[tex]L=x-\frac{1}{2}[/tex]
Therefore, this is the length of the glass pane.
