Question Video: Identifying the Rectangle with the Greatest Perimeter

The diagram shows the floor plan of David’s house. Which of the shaded rectangular rooms has the greatest perimeter?

03:37

Video Transcript

The given diagram shows the floor plan of David’s house. Which of the shaded rectangular rooms has the greatest perimeter?

This picture or diagram shows the floor plan of David’s house. It’s like a map of all the different rooms. Are we’re looking down on it to see the different shapes. In this question, we’re looking in particular at the shaded rectangular rooms. So we’re thinking about Matthew’s bedroom, David’s bedroom, and also the kitchen over here. And we’re asked which one of these has the greatest perimeter. Now we know that the perimeter of a shape is the distance all around it. So we could actually read the question like this, which of the shaded rectangular rooms has the greatest distance around it?

Now imagine for a moment that we’re standing in each of these rooms one by one. We wouldn’t be thinking about the size of the room in the way that we’d normally look at a room and think, that’s a big room. If we were trying to do this in real life, we’d probably have a tape measure of some sort and we’d be measuring the distance all around the room. Just because our room looks big doesn’t necessarily mean it’s got the largest perimeter. Well, we don’t need to use a tape measure to find the answer; we’re not standing in the rooms. We’ve got a floor plan to help. And so what we’re going to have to do is to count the lengths of the squares that go all the way around. We could call these squares units.

Let’s start by measuring the perimeter of the kitchen. The longest side here is six units long, and this shorter side is two units long. Then we’ve got another long side of six and another shorter side of two. This is interesting, isn’t it? We’ve got two lots of six and two lots of two. This shows us what we know about rectangles, doesn’t it? They have two pairs of equal sides. We know that six plus two equals eight. And if we had another lot of six plus two or another lot of eight, we get a total of 16 units altogether. The distance all around the kitchen is 16 units.

Now let’s measure the perimeter of Matthew’s bedroom. This side here is three squares long. Then this longer side is four squares long. Then just like before, we have another lot of three and another lot of four. We know that three plus four equals seven. And so if we had another lot of three plus four or another lot of seven, we get double seven, which is 14. The distance all around Matthew’s bedroom is 14 units.

Now let’s measure the perimeter of David’s bedroom. This side here is four units long. This longest side along the top is six units long. We know that four and six make 10, don’t we? Can you guess what the whole perimeter is going to be? We have another side of four and another side of six. As we’ve said already, four plus six equals 10. And if we add another lot of four plus six or another lot of 10, we get double 10, which is 20.

By counting the square lengths or the units all the way around these shaded rectangular rooms, we found which room has the largest perimeter. The perimeter of the kitchen is 16 units. The perimeter of Matthew’s bedroom is 14 units. But the perimeter of David’s bedroom is 20 units. Out of the three shaded rectangular rooms, the one that has the greatest perimeter is David’s bedroom.

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