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## Area versus perimeter

# Area & perimeter word problem: dog pen

CCSS.Math:

## Video transcript

Mike built a rectangular
dog pen that is 21 feet long and has a perimeter of 78 feet. What is the width
of Mike's dog pen? So let's draw what
it might look like. So it might look
something like this. I'll do my best to draw it, a
rectangle or potential dog pen. So let's say that this is
the dog pen right over here. And they give us its length. Its length is 21 feet. So this distance right
over here is 21 feet. And of course, if that
distance is 21 feet, this distance is also
going to be 21 feet. Now, they also tell us that
the perimeter is 78 feet. So the perimeter is 78 feet. So we need to figure
out the width. And the width would be this
length-- or this width, I should say-- this
width, which is going to be the same thing as
that width right over here. So let's think about. And we know how we
figure out the perimeter. If we added this
distance, 21 feet, to this distance, the width,
plus 21 feet to the width again, we're going
to get to 78 feet. So one way to back into
what the width is is to say, well, look if we sum up
all of these lengths, we're going to get 28 feet. So let's at least subtract these
two orange lengths, the two 21 feet, from the 78 feet. And then we figure out how
much length essentially these two widths
have to make up. So let's subtract. Let's do 78 minus 21 minus 21. And what's that
going to be equal to? So that's 78 minus 42. And 78 minus 42-- I don't want
to make a careless mistake-- 78 minus 42 is going
to get me to 36. So this is equal to 36. And let's remind
ourselves what 36 feet is. That's the total length-- or
I should say the total width-- if we were to take the
width down here and add it to the width up here. Now, we know something else. These are the exact same
width, that this distance is the same as this distance. And if we add them
together, we get to 36. So what are two
distances, or what are two numbers that I can
add together to get to 36? Well, we know that 18
plus 18 is equal to 36. So this one down
here must be 18. And this one up here
must also be 18. And we can verify that. Try adding all of
these up together. You add the two widths. You get 18 plus 18. And you add the two
lengths, plus 21 plus 21. And you are left with 36, which
is exactly what we got here. This is what we needed the two
widths to add up to-- plus 42. Which is, of course,
equal to-- 36 plus 42 is equal to 78,
which is the perimeter.