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