00:01
So we're told that the farmer has 2 ,600 feet of fencing.
00:06
That would be the perimeter.
00:08
And we have it bordering based on the picture, this field.
00:21
So if the perimeter is the sum of the sides, this perimeter would be two x plus y or 2 ,600 would equal two x plus y.
00:33
The area is still the product of the sides.
00:38
So the area is x times y, even though one side is the road.
00:42
So if i wanna take area and write it in terms of x, i need to take this perimeter formula and solve for y.
00:51
So i do that by subtracting two x from both sides and i substitute in for y that value.
01:04
So now i have a formula for area that only has one variable, multiply through the x, and that's my formula.
01:15
Now, notice this is a parabola.
01:23
If i thought about this in terms of drawing the parabola graph, i have two values of x that wouldn't give me a completed fence.
01:32
And this one in the middle, that's my vertex.
01:35
My vertex is the value that's gonna maximize the area because this graph would be the total area versus our x value...