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.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> 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.      Log On


   

Question 902637: 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.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

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 ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B16x%2B-44+=+0) has the following solutons:

  

  x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

  

  For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

  

  First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2816%29%5E2-4%2A3%2A-44=784.

  

  Discriminant d=784 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-16%2B-sqrt%28+784+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+784+%29%29%2F2%5C3+=+2

    x%5B2%5D+=+%28-%2816%29-sqrt%28+784+%29%29%2F2%5C3+=+-7.33333333333333

    

    Quadratic expression 3x%5E2%2B16x%2B-44 can be factored:

  3x%5E2%2B16x%2B-44+=+3%28x-2%29%2A%28x--7.33333333333333%29

  Again, the answer is: 2, -7.33333333333333.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B16%2Ax%2B-44+%29