A storage box has a volume of 4368 in cubed. the length is 24 in and the height is 1 in more than the width. Find the height and width of the box. Solve by factoring

Question

anonymous · Answer

Well, here you could set the width to equal x, and the height to equal x+1. That would leave you with 24x(x+1)=4368. You would distribute, and come up with 24(x^2)+24x=4368. Here you can subtract and set it equal to zero, leaving you with 24(x^2)+24x-4368=0. There are numerous factors that lead to -4368, but for this we can use the quadratic formula. $$x=-b \pm \frac{ \sqrt{b^{2}-4ac} }{ 2a }$$

anonymous · Answer

With b=24 here, we would have $$x=-24 \pm \frac{ \sqrt{24^{2}-4(24)(-4368)} }{ 4(24) }$$

anonymous · Answer

Apologies, I wrote that wrongly. We would end up here with $$x= \frac{ -24 \pm 648 }{ 48 }$$
doing this, we end up with x=13 and x=-14. Because you cannot have a negative side, x=13 for the purposes of this problem. You can verify this by multiplying: (13)(13+1)(24)=4368. It does check. So we know here that the width is 13 units and the height is 14 units.

anonymous · Answer

But by factoring with these xs, you would end up with 24(x+-3)(x+14)