Here we know that Karen was trying to factor the following expression:
[tex]6x^2+106x[/tex]
And we want to find the width of Karen's area model, so we can say that that expression represents the area of a rectangle, so if we name (A) as this area, then:
[tex]A=6x^2+106x \\ \\ \\ \text{Taking 2x as common factor}: \\ \\ A=2x(3x+53)[/tex]
Recall that the area of a rectangle is defined as:
[tex]A=L\times W \\ \\ \\ Where: \\ \\ L:Length \\ \\ W:Width[/tex]
So we can say:
[tex]W=2x \\ \\ L=3x+53[/tex]
Finally, the width is:
[tex]\boxed{2x \ units}[/tex]
