00:01
Hi there, so for this problem, we have a rectangular storage area that is to be constructed along the sides of a tall building.
00:09
So let me just put in blue in here, this is the building.
00:15
Okay, and then a security fence is required along the three remaining sides of the area.
00:22
So let me just draw that situation for this, something like this, let's label the dimensions of this as x, y and y.
00:34
Okay, now what is the maximum area that can be enclosed with 100 meters of fencing? so the perimeter for this is 1000, okay, sorry, 1000 meters, okay? now the perimeter is the sum of all of the sides.
00:50
As you can see from the picture, we have two sides y and one side x.
00:54
Now we know that when we want to maximize in this is the area, the area for this is just x times y.
01:00
Now from the perimeter, we're gonna solve for x, so that will be 1000 minus two times y, and then we substitute that into the area.
01:08
When we do that, when we substitute that into the area, we will have then 1000 times y minus two times y squared...