Answer: the length is 11 cm.
The width is 7 cm.
Explanation:
Let L represent the length of the rectangular plastic box.
Let W represent the width of the rectangular plastic box.
The area of the rectangular top of the box is 77 square cm. This means that
LW = 77- - - - - - - ;- - - -1
The plastic box has a length 4 cm longer than its width. This means that
L = W + 4
Substituting L = W + 4 into equation 1, it becomes
(W + 4)W = 77
W² + 4W = 77
W² + 4W - 77 = 0
W² + 11W - 7W - 77 = 0
W(W + 11) - 7(W + 11) = 0
W - 7 = 0 or W + 11 = 0
W = 7 or W = - 11
Since the width cannot be negative, then W = 7cm
L = 77/7 = 11 cm