Area versus perimeter
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.