Step-by-step explanation:
Area = length x width
let x represent the width of the rectangle
[tex]84 = x \times (x + 5)[/tex]
[tex]0 = {x}^{2} + 5x - 84[/tex]
[tex]0 = (x - 7)(x + 12)[/tex]
therefore
[tex]x = 7 \: \: or \: - 12[/tex]
however since length cannot be negative, the width is 7.
width = 7
length = 7+5
= 12
