00:01
So in this problem, we're told that cynthia's currently to try and get a rug, and we know that the dimensions of the room, so i apologize, this isn't for the rug, this is for the room.
00:09
The dimensions of the room are 18 feet by 25 feet.
00:14
Now, inside the room, once she puts the rug down, she's going to have a strip of the floor in uniform length.
00:20
The other piece of information, we're told, is the total square feet of the rug is 368 square feet.
00:26
We want to know the dimensions that she can buy for the rug.
00:30
Well, in this case, let's set up what are a picture.
00:33
So we set up a picture, we have our rectangle, and we know that the rectangle is 18 feet wide by 25 feet long.
00:41
Now, here's what they mean by the rug.
00:43
The rug is going to be inside the room, and if it's going to be a uniform width, that means the distance from each of the sides to the edges are going to be the same distance.
00:53
And because we don't know them, we're going to call it x.
00:56
So now what we need to do is represent the length and width of the rectangle or of the rug.
01:03
Well, if this holds inside length at the top is 25 feet, notice how we cut two sides of length x off.
01:11
So to find the length of this rug, it would be 25 minus 2x.
01:17
Then, kind of the same idea in the opposite direction, the width was 18 feet, but again, we cut off x -inch, x feet on both sides.
01:25
So the width would be 18 minus 2x.
01:28
Well, to find the area, we need to multiply the length times the width, and it should equal to the total number of square feet, which is 368.
01:37
So now we just need to solve this equation for x.
01:40
So first, we need to multiply the two binomials.
01:43
Well, 250 times 18 is equal to 450.
01:47
Let's make that of 5.
01:48
Then we have 25 times negative 2x, which is negative 50x.
01:53
Negative 2x times 18 is negative 36x.
01:56
And then negative 2x times negative 2x is positive 4x squared.
02:01
And this is equal to 368.
02:03
Well, now what we need to do is put this in standard form.
02:07
So i'm going to take my x squared term and put it first.
02:11
Then we'll combine our like terms.
02:13
Negative 50x minus 36x is negative 86x.
02:17
And then at the same time, i'm going to subtract 368 from both sides.
02:21
So that way you'll be set equal to 0.
02:24
Well, 450 minus 368 is equal to positive.
02:27
Positive 82.
02:29
All right.
02:30
So now what we need to do is we're going to solve this by factoring...