SOLUTION: A square base box has a volume of 200cm, find the dimensions if the height is 3cm more than the length

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Question 1183488: A square base box has a volume of 200cm, find the dimensions if the height is 3cm more than the length
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
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A square base box has a volume of 200 cm^3, find the dimensions if the height is 3 cm more than the length
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According to the condition, for the squared base side x, we have this cubic equation


    x^2*(x+3) = 200   cubic units (the volume).



One solution is easy to guess:  x = 5.


Now, since the left side of the equation is monotonically increasing function, this solution x = 5 is UNIQUE:

there are no other solutions.


ANSWER.  The dimensions are 5 cm for the square base and 8 cm for the height.

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The dimensions of the box are x, x, and x+3; the volume is 200.



There are no easy ways to solve that cubic equation algebraically; so let's solve the problem informally.

The volume is given to be (EXACTLY) 200. That means the dimensions of the box are almost certainly whole numbers.

So look at the prime factorization of 200 and find a way to group the factors so that they match the pattern x, x, and x+3.

200 = 2*2*2*5*5 = 5*5*(2*2*2) = 5*5*8 = (x)(x)(x+3)

ANSWER: x=5; the dimensions of the box are x, x, and x+3, which is 5, 5, and 8.
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