Mike built a rectangular dog pen that is 21 feet long,
and it has a perimeter of 78 feet.
What is the width of Mike's dog pen?
So let's try to draw this dog pen.
So it's going to have some width,
and I'll just label that as the width.
And it's going to have a length of 21 feet.
So this distance right over here is going to be 21,
and of course, this is as well.
It's a rectangle, so this is also
going to be a distance of 21.
And of course, this distance down here
is also going to be the width.
Now, how do you calculate the perimeter of this?
They tell us that the perimeter is 78 feet,
but how do we calculate the perimeter using
this information?
Well, the perimeter is just the sum
of these two widths and these two lengths.
So the perimeter is going to be the width plus the width
plus the two lengths, plus 21 plus 21.
This will give us the distance if we
go around this rectangular dog pen.
And they tell us that this thing needs to be equal to 78 feet.
Let me do the same color.
Now, we could simplify this expression
on the left hand side a little bit.
We know that the width plus the width plus the sum of the two
lengths-- which are both the same-- plus 42
is going to equal 78.
So what must the width plus the width be equal to?
So, I have something-- I have this thing
plus 42 is equal to 78.
So if I have something plus 42 is equal to 78,
that means that this something must be 78 minus 42.
So let's write that down.
Width plus width is going to be equal to 78 minus 42,
which is-- I'll do it in a new color-- 78 minus 42 is 36.
And you can verify this.
If this thing right over here is equal to 36,
if the sum of my two widths-- or essentially
this is 2 times the width.
If 2 times the width is 36, then width plus width is 36.
Then this right over here is 36.
36 plus 42 is indeed equal to 78.
So we figure out a width so that if I add the width to itself,
I get 36, because when we add those two, you get 36,
plus 21 plus 21 is equal to 78.
So what number plus itself is going to be equal to 36?
Another way to rewrite this is a number plus itself
is the same thing as 2 times that number.
So 2 times the width is going to be equal to 36.
And later on when we learn algebra in a little bit
more detail, you'll see that essentially what we're doing
is actually algebra, but it just comes out of common sense,
out of logic.
So if I say 2 times some value is equal to 36,
what is that value going to be?
Well, 2 times 18 is 36, so the width is equal to 18.
And you might say well, how did I figure out
that the width is equal to 18?
Well, there's a couple of ways to think about it.
If 2 times the width is equal to 36,
then the width must be equal to 36 divided by 2,
must be equal to 36 over 2, which would also get you 18.
So there's a lot of ways to think about it,
and later on when we learn algebra in a little bit
more details, things like this will seem even more obvious.
But I just wanted to show you that you can actually
reason this through just with what we know about perimeter.