+0  
 
0
63
1
avatar+194 

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?

 Jul 28, 2020
 #1
avatar+27970 
+1

Since we are looking for 'h' , let's put dimensions in terms of 'h'

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    

 Jul 28, 2020

49 Online Users