SHORT ANSWER: 84cm
Let width = w
Let length = w + 5
The area of a rectangle is found by multiplying its width by length and the problem states that the area is 84 cm2.
(Width)(Length) = 84
(w)(w + 5) = 84
w2 + 5w = 84
w2 + 5w - 84 = 0
(w + 12)(w -7) = 0
w + 12 = 0
w = -12
The width of a rectangle can't be NEGATIVE!!! Forget about that!
w - 7 = 0
w = 7
Now go back to naming the variables and replace the w with 7.
Length = w + 5 = 7 + 5 = 12
Width is 7 cm. Length is 12 cm.
Check it. Is 7 x 12 = 84? Yes.