Question 1183488
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The dimensions of the box are x, x, and x+3; the volume is 200.<br>
{{{V = (x)(x)(x+3) = x^3+3x = 200}}}<br>
There are no easy ways to solve that cubic equation algebraically; so let's solve the problem informally.<br>
The volume is given to be (EXACTLY) 200.  That means the dimensions of the box are almost certainly whole numbers.<br>
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.<br>
200 = 2*2*2*5*5 = 5*5*(2*2*2) = 5*5*8 = (x)(x)(x+3)<br>
ANSWER: x=5; the dimensions of the box are x, x, and x+3, which is 5, 5, and 8.<br>