00:02
A farmer has 300 feet of fence available to enclose a 4500 square feet region in the shape of adjoining squares, like shown in the figure, with sides of length x and y.
00:20
We want to find those values of x and y.
00:24
So we have this sketch here of the field or region, and we have two squares.
00:35
The upper square let's say have lens had sides of lens y this square here and the other square bigger one in this case is sketch we have x written y if we change the empty same doesn't matter and then the biggest square which is in this case below the other has sides of lens x then we have to find x and y for that we're going to notice that we have two information here one is the area of the region here 4 ,500 square feet is the area of the region so the area of the region means the whole this case blue area or what is the same is some of the areas of the squares.
01:57
Here we have the region equal 4 ,500 square feet.
02:07
Okay, that's one information.
02:09
The other one is that we have 300 feet of fence.
02:16
That is the perimeter of the region is equal to 300.
02:23
That's what we have from that part of the region equal to 300.
02:36
Equals 300 feet.
02:41
Because we want to put the fence all around the region that is following the border, the frontier of the region.
02:55
So that's exactly what we call perimeter, that is the sum of the lands of the sides of the region.
03:05
So we can see in this sketch that we have all the elements to calculate that and there is another part we don't have mark in this draw here is this side here and that side is we can see is this whole length minus this length here that is is x minus y and with this information here is a positive value as it should be so with this information we're going to write two equations which are area of the region equal 45 ,000.
04:08
And we take out the units, we know it's gonna be correct at the end, but we can check it out after the calculations.
04:17
And that gotta be equal to the area of the sum of the areas of the squares.
04:23
That is x square, the area of the lower square, plus the area of the smaller square, which is y square.
04:36
So this is the first equation we have and the other is perimeter of the region equal 300 and now we get to find that in terms of all the length on the border of the region that is three times x here here and then plus three times y here here here and here and plus this side i calculated finally here is x minus y and now we have all the borders of the region and then the two equations are x squared plus y square equal 4500 and the other is that simplify a little bit 3x plus x is 4x 4x plus 2 y equal 300.
05:57
That can be simplified as x squared plus y square equal 500.
06:03
The second one we can divide by two both sides and we get 2x plus y equal 150.
06:14
So what we're going to do here is to take the second equation which is linear and we solve for y.
06:24
From 2x plus y equal 150 we can get y equal 150 minus 2x.
06:41
So we plug in, plug in this into the first equation.
07:06
We have that.
07:09
And this equation i'm talking about here is this one here...