00:01
Okay, so we have a 100 -foot stone wall, and that looks to be represented just right here.
00:10
And we want to continue making a fence all the way around.
00:18
All right, and what i need to do is i have to figure out how to get the greatest possible area.
00:26
All right.
00:26
Now, my other piece of information i have is that i have 900 feet of fencing.
00:31
Okay, so everything that i have highlighted in the green needs to be equal to 900.
00:39
So let's figure that part out first.
00:41
So i have my 900 equals.
00:44
Now, my 100 feet, my first 100 feet is in yellow.
00:47
I don't need fencing for that.
00:49
Okay, so i'm going to have my x, right, from here.
00:53
All right, then plus my w, which would be here.
00:58
Okay, now the bottom is not going to just be x.
01:01
That's 100 plus x so i'm going to have plus 100 plus x and then finally completing the wall i'm going to have another w so plus w all right now i want to simplify this a little bit um so let's see we're going to have 900 is equal to now i got two different xes here so we'll say 2x all right plus i i also have two different ws, so plus 2w, and then plus 100.
01:34
All right, now let's simplify this a little bit.
01:36
I'm going to start by subtracting 100 from both sides.
01:40
So that will give me 800 is equal to 2x plus 2w.
01:45
And then i can divide everything by 2, so that gives me 400 is equal to x plus w.
01:53
All right, and so this is as simplified as i can make the expression right now.
01:57
Okay, now this problem, we want to maximize the area, the greatest possible area.
02:05
And so i'm going to come off to the side here.
02:07
I need to think about how do i get the area? the area is the length, which is 100 plus x, times our width, which we just have is w.
02:21
All right, i can leave the equation in this form, or i can distribute.
02:27
I think i'm going to leave it as is right now.
02:31
Now, to solve this problem, what i need to do is i need to solve for one of these variables here.
02:36
So i need to solve for a variable.
02:42
And to be honest, it doesn't really matter which one it is.
02:45
I think i'm just going to solve for x.
02:47
So i'm going to say x is equal to 400 minus w...