The correct option will be : B) 6 cm.
Explanation
Suppose, the width of the rectangle is [tex]x[/tex] cm.
As, the length is 6 cm longer than the width, so the length will be: [tex](x+6) cm.[/tex]
Formula for the Area of rectangle is: [tex](Length)*(Width)[/tex]
Given that, the area of a rectangle is 72 cm²
So....
[tex]x(x+6)=72\\ \\ x^2+6x-72=0\\ \\ (x+12)(x-6)=0[/tex]
Using zero-product property, we will get...
[tex]x+12=0\\ x= -12[/tex] (Negative value is ignored as width can't be negative)
and
[tex]x-6=0\\ x=6[/tex]
So, the width of the rectangle is 6 cm.
