Question 259834: A box with rectangular sides has width twice the length of the base. The volume is 24 cubic inches and the total surface area of all six sides is 52 square inches. Write down a (cubic) equation whose solution is the length of the box.
Use L for the length of the box.
Equation: 0 =
I know the base would be L2 and the sides would be 2L*L and since there are 2 bases it would be 2(2L) and four sides 4(2L^2), but I do not really know where to go from there. Any help would be great, thanks!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let
L = Length, W = Width, H = Height
Recall that the formula for the volume of the box is:  (ie multiply the length, width, and height to find the volume)
In addition, the surface area is simply the sum of the individual areas of the 6 faces on the box. Since there are essentially 2 of each face, we have the basic surface area formula
Surface Area = 2*Length*Width+2*Width*Height+2*Length*Height
which can be rewritten as 
Now because "A box with rectangular sides has width twice the length of the base", we can say that  (ie double the length to get the width)
So for each equation above, we can plug in to eliminate W altogether. What will result will be two equations with two unknowns (which is now possible to solve, if there is a solution).
So plug in into to get  . Also, plug in  (the given volume) to get  . This will be equation 1.
Now plug in into to get  . Also, plug in  (the given surface area) to get  . We'll refer to this as equation 2.
So you should now have the system of equations
To solve this system, simply isolate one variable and use substitution. I'll let you finish the problem. Let me know if you still need help.
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