00:01
We're told we have a rectangle, say here's our rectangle, and let's label x and y, say x and y.
00:08
Now, we want the dimensions of the rectangle with area 225.
00:15
Well, that's x times y.
00:17
So i could solve for x or y.
00:19
Let's say y equals 225 over x.
00:24
And then we have a constraint, and that's it.
00:28
What we want to do is minimize the perimeter.
00:30
So the perimeter is just going to be 2x plus 2y.
00:37
Well, we solved for y.
00:41
So that perimeter is going to be 2 times x plus 2 times y.
00:47
Well, that's 2 times 225 over x, which is 450 over x.
00:53
And i'm going to write that as x to the negative 1 because the next step is to take the derivative.
00:58
So that's going to be 2 minus 450 x to the negative 2.
01:05
And we set that equal to 0.
01:08
I'm going to multiply by x squared to get 2x squared minus 450 equals 0...