Question 1147958
<br>
height: x
width: x-3
length: x+3.5<br>
volume = length * width* height<br>
{{{x(x-3)(x+3.5) = 561}}}<br>
Probably solve using a graphing calculator....<br>
Or, if you are really good with mental arithmetic, solve by trial and error:<br>
561 = 11*51 = 3*11*17<br>
The problem says two of the dimensions differ by 3; and the factors 11 and 17 differ by 6.  That might lead you to<br>
3*11*17 = 12*(11/2)*(17/2)<br>
And those dimensions satisfy the conditions of the problem:
x = 17/2 = 8.5
x-3 = 11/2 = 5.5
x+3.5 = 17/2+7/2 = 24/2 = 12<br>
ANSWER: the height of the box is x = 8.5 inches.<br>