00:01
In this exercise, we want to find the dimension of the box where we have a volume of 108 cubic inches.
00:05
We have the length equals three times the height, and the height is one inch less than the width.
00:09
So we know volume 108 equals length times height times width.
00:14
So how about we replace two of these so that we have a function that has all the same variable.
00:20
So let's say we kept the length as it is.
00:26
So, or actually we kept the height as it is.
00:29
If we cut the height as it is, we have one, zero eight equals, replace length with 3h, keep h, and replace w.
00:36
If we add one to both sides of this, we get h plus 1 equals w.
00:40
Place w with h plus 1.
00:42
So we're looking for the height.
00:44
Now, if we multiply this together, we have 3h squared times h plus 1.
00:48
That becomes 3h cubed plus 3h squared equals 108.
00:54
If we subtract from both sides 108, we have an equation that we can solve for, 3h2.
00:59
Cubed plus 3h squared plus minus 108 equals 0 we want to solve for 0.
01:05
So let's go to the next page...