00:01
All right, we're looking at an area problem with a bunch of unknowns.
00:06
So to start off, when we think about the length and the width, we know that the length of the rectangle is 2 inches wider than, or 2 inches longer than its width.
00:22
So the length equals the width plus 2.
00:28
And then here's our width.
00:31
So to come up with the area of this, the area of our rectangle is equal to the length times the width.
00:40
And we actually know that that we know one other piece here, and that is that the area of the rectangle is 12 inches more than three times the perimeter.
00:51
So a couple of the things to kind of think about here.
00:55
The perimeter is two times the length plus two times.
01:01
The width.
01:03
So if we know that the area here is equal to three times the perimeter plus 12 more inches, this gives us a lot of different variables here that we can substitute in and come up with an actual equation for.
01:20
So first thing, let's let's set equal our length and width here.
01:25
I'll use blue just to kind of get us started.
01:27
So length and width, we know that that is our area.
01:32
And that's equal to three times the perimeter.
01:35
So three times, we'll say our perimeter, which is, i'll do it in red, two times the length plus two times the width.
01:46
Again, that's just the distance around the object, plus 12.
01:50
All right, let's start doing some substitutions now so that we can get everything in terms of one variable.
01:56
So our length is equal to the width times two.
01:59
So we can say the width plus two times the width.
02:06
That's our length is w plus two.
02:08
And that equals three times two times the length, which again is the width plus two, plus two times the width plus 12.
02:21
All right.
02:22
Lots of simplifying to do.
02:24
So on the left hand side, w times w is w squared, the width squared, plus two times the w and then working our way from inside out we'll have three times two times w so 2 w plus two times two which is four plus 2 w plus 12 combining some like terms here we've got 2 w and another 2 w here so that's 4 w and i'm going to kind of roll with that as we get into the next simplifying step so we've got w squared plus 2 w is equal to three times this group here.
03:12
So 3 times 4 w is 12 w and 3 times the 4 that's left over is just 12.
03:19
So 12 w plus 12 plus the 12 that was outside of the whole group.
03:26
So that's another 12...