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The total surface area of a box is 100. The length of the box is twice its width, as well as 3 less than its height. How many units are in the height of the box?

 Mar 13, 2020
 #1
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Call the width:  W

Call the length:  L               The length is twice the width:  L = 2W

Call the height:  H              The length is 3 less than the height:  L = H - 3   --->   H = L + 3   --->    H  =  2W + 3

 

The total surface area = 100.

The total surface ares  =  2LW + 2LH + 2Wh  =  100 

     --->   LW + LH + WH  =  50

Substituting:

     --->   2W·W + 2W·(2W + 3) + W·(2W + 3)  =  50

     --->            2W2 + 4W2 + 6W + 2W2 + 3W  =  50

     --->                                     8W2 + 9W - 50  =  0

     --->                                  (8W + 25)(W - 2)  =  0

     --->     W = 2     or     W = -25/8   (impossible)

     --->     W = 2     and     L = 4     and    H = 7

 Mar 13, 2020
 #2
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THANK YOU SO MUCH!!!

 Mar 13, 2020

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