00:01
All right, we're going to solve problem 20 in this problem.
00:06
Let's say that the dimensions of square -based box be x, comma y, comma z, all right? and we know that the sum of these three dimensions is going to be equal to 108.
00:19
So, x plus y plus z is equal to 108.
00:24
Since we're talking about square -based box, that means the base is square, which means the dimensions, the two of the dimensions are going to be equal to each other.
00:36
So let's say x is equal to y, and this expression is going to be equal to x plus x plus z is equal to 108.
00:46
And from here, 2x plus z is equal to 108.
00:50
So that's my first equation.
00:52
And we'll try to figure out the greatest volume with these three dimensions.
00:58
Okay.
00:59
And the volume of this square base box can be found by this formula x times y times z if i multiply all these dimensions and for here if i solve this the first equation for z we get z is going to be equal to 108 minus 2x and we're going to plug this back into this formula for z and the volume is going to be equal to x times x.
01:26
Remember that x was equal to y.
01:29
X times x times 108 minus 2x.
01:33
So if i simplify this expression, we get volume is equal to x squared times 108 minus 2x.
01:42
And let's try to distribute this x squared into the parentheses.
01:46
So we get v is going to be equal to 108 x squared minus 2x so if i try to figure out the greatest volume with this given dimensions, so i need to focus on v prime x and set it equal to 0...