SOLUTION: 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 (cu

Algebra ->  Algebra  -> Rectangles -> SOLUTION: 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 (cu      Log On

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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(28549) About Me  (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: V=LWH (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 S=2LW%2B2WH%2B2LH


Now because "A box with rectangular sides has width twice the length of the base", we can say that W=2L (ie double the length to get the width)


So for each equation above, we can plug in W=2L 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 W=2L into V=LWH to get V=2L%5E2H. Also, plug in V=24 (the given volume) to get 24=2L%5E2H. This will be equation 1.


Now plug in W=2L into S=2LW%2B2WH%2B2LH to get S=4L%5E2%2B4LH%2B2LH. Also, plug in S=52 (the given surface area) to get 52=4L%5E2%2B4LH%2B2LH. We'll refer to this as equation 2.


So you should now have the system of equations

system%2824=2L%5E2H%2C52=4L%5E2%2B4LH%2B2LH%29


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.