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3 years ago

10

A plastic box has a length 4 cm longer than its width. The area of the rectangular top of the box is 77 square cm. Find the leng

th and width of the box.

1 answer:

finlep [7]3 years ago

4 0

Answer: the length is 11 cm.

The width is 7 cm.

Step-by-step 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

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