00:02
In this problem, we know that the farmer is going to put 300 feet of fencing around a rectangular field.
00:09
We know that the area of the field is 5 ,000 square feet.
00:13
So we're looking for the dimensions of the field.
00:17
So let's suppose that one of the dimensions is x and the other is y.
00:23
So the perimeter has to be 300 feet because that's how much fencing we have.
00:28
So we can say that 2 times x plus 2 times y equals 3.
00:33
To get the perimeter, you add all the sides.
00:36
That would be 2 x's and 2 y's.
00:38
We can divide this equation by 2 and we have x plus y equals 150.
00:45
Okay, now let's work on the area part.
00:48
So we know the area of a rectangle is length of width, so area equals x times y.
00:54
And for this problem, we know the area is 5 ,000, so 5 ,000 equals x times y.
00:59
Now we need to eliminate a variable, and that's why we have the perimeter equation.
01:03
If we take this equation and we isolate y, we have y equals 150 minus x.
01:10
And we can substitute that into our other equation, and we have 5 ,000 equals x times 150 minus x...