The surface area of a box is 160. the length of the box is twice its width as well as 4 less than its height. how many units are in the height of the box? (the surface area of a box is the sum of the areas of all 6 of its rectangular faces.) aops

Width = n
Length = 2n
Height = 2n + 4
2 (n x 2n) = 4n^2
2 (n x (2n + 4)) = 4n^2 + 8n
2 (2n x (2n + 4)) = 8n^2 + 16n

4n^2 + 4n^2 + 8n + 8n^2 + 16n = 160
16n^2 + 24n = 160
(Divide everything by 8)
2n^2 + 3n = 20
2n^2 + 3n - 20 = 0
(2n - 5)(n + 4) = 0

n = 2.5 Or n = -4

However n can not be less than 0

So n = 2.5
Height =2n +4
=2(2.5) +4
=5+4
=9

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