SOLUTION: An open box​ (with no​ lid) has a square base and four sides of equal height. The height is 2 greater than the length and width. What are the dimensions of the box if t

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Question 1094819: An open box​ (with no​ lid) has a square base and four sides of equal height. The height is 2 greater than the length and width. What are the dimensions of the box if the volume is 96 cubic inches and the surface area is 112 square​ inches?
What is the width​ (and length) of the​ box?
What is the height of the​ box?
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


V+=+l%2Aw%2Ah+=+%28x%29%28x%29%28x%2B2%29+=+96

For the volume and surface area to be whole numbers, it is almost certain that all the dimensions of the box are whole numbers. So do some trial and error to find that x=4.

So the length and width of the square base are 4, and the height is 6.

You can confirm that those measurements make the surface area 112; but it is not necessary.

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Bottom dimensions x and x.
height y.
y=x%2B2, ;
y%2Ax%5E2=96
and just those should be enough without using the surface area description x%5E2%2B4xy=112.

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%28x%2B2%29%2Ax%5E2=96
x%5E3%2B2x%5E2-96=0
One of the solutions is x=4.
This would make highlight%28system%28x=4%2Cy=6%29%29



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check
6*4*4=96?
24*4=96
96
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4^2+4*4*6=112?
16+4*24=112
16+96
112
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Both conditions work.