00:01
Okay, so for this problem, we need to find the dimensions of a box with a volume of 108 cubic inches.
00:09
So we know that the volume formula for a box is length times, one times height, and we know that length times what times high for this box is 108.
00:19
We're also told that given a height, h, that the length is three times the height, so l is equal to 3h, and that the width is one more than that.
00:32
The height because the height is one less than the width.
00:36
So w equals h plus one.
00:38
And given this information, we can go ahead and rewrite our formula in terms of h.
00:48
So l is 3h, w is h plus 1, and h is just h equals 108.
01:00
We combine this, we get 3h squared times h plus 1, is equal to 108.
01:09
If we multiply again, we get 3h cubed plus 3h squared minus 108 is equal to 0.
01:20
If we divide both sides by 3, we get h cubed plus h squared minus 36 is equal to 0.
01:31
From here, we can use the rational zero theorem to produce a pool of integers that could possibly work with our equation.
01:42
And so we know that these integers need to be positive integers because we're dealing with a box and a negative measurement wouldn't make no sense...