SOLUTION: the length of a closed box is 3 times its height, and it is 4 cm wide. if the total surface area is 88 cm^2, find the dimensions of the box.

 

Hi,

.

Surface = 2lw + 2lh + 2wh

Surface = 2(3h)4 + 2(3h)h + 2*4h = 88cm^2

 6h^2 + 24h + 8h -88 = 0

6h^2 + 32h - 88 = 0

 3h^2 + 16h - 44 = 0 (Tossing out the negative solution for unit measure)

h = 2cm

l = 6cm

w = 4cm

Surface = 2lw + 2lh + 2wh = 48 + 24 + 16 = 88

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation  (in our case ) has the following solutons:

  

  

  

  For these solutions to exist, the discriminant  should not be a negative number.

  

  First, we need to compute the discriminant : .

  

  Discriminant d=784 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 2, -7.33333333333333.
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