A box has a total surface area of 100. The length of the box is equal to twice its width, as well as equal to 3 less than its height. What is the height of the box?
Since we are looking for 'h' , let's put dimensions in terms of 'h'
l = h-3
l = 2w or 1/2 l = w so w = 1/2(h-3)
surface area = 2 (lh) + 2 wh + 2 wl
2 ((h-3)(h) + 2(1/2h-1.5)(h) + 2 (1/2h-1.5)(h-3)
2 h^2 - 6h + h^2- 3h + h^2-6h+9
4 h^2 -15h+9 = 100
4 h^2 -15h-91 = 0 Quadratic formula shows h = 7