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# 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. Wh

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A box has a total surface area of  The length of the box is equal to twice its width, as well as equal to  less than its height. What is the height of the box?

Jul 13, 2020

#1
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Did you directly copy it from somewhere else without proofreading over it?

Please do not, because the LaTeX may mess up.

Let length = L, width = W, height = H.

$$2(LW + WH + HL) = 100\\ L = 2W\\ L = H - 3$$

Changing the subjects of the second and third equations,

$$W = \dfrac L2\\ H = 3 + L$$

Substituting these into the first equation:

$$2\left(L \cdot \dfrac L2 + \dfrac L2 \cdot (3 + L) + (3 + L) \cdot L \right) = 100\\ L^2 + 3L(3 + L) = 100\\ 4L^2 + 9L - 100 = 0$$

Solving by quadratic formula gives $$L = 4$$

I believe you can work out the width and the height from here.

Jul 13, 2020
#2
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thank you! i got it now. sorry i will proofread next time

Jul 13, 2020