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The given diagram shows the floor plan of David’s house.
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Which of the shaded rectangular rooms has the greatest perimeter?
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This picture or diagram shows the floor plan of David’s house.
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It’s like a map of all the different rooms.
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Are we’re looking down on it to see the different shapes.
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In this question, we’re looking in particular at the shaded rectangular rooms.
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So we’re thinking about Matthew’s bedroom, David’s bedroom, and also the kitchen over here.
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And we’re asked which one of these has the greatest perimeter.
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Now we know that the perimeter of a shape is the distance all around it.
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So we could actually read the question like this, which of the shaded rectangular rooms has the greatest distance around it?
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Now imagine for a moment that we’re standing in each of these rooms one by one.
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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.
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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.
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Just because our room looks big doesn’t necessarily mean it’s got the largest perimeter.
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Well, we don’t need to use a tape measure to find the answer; we’re not standing in the rooms.
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We’ve got a floor plan to help.
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And so what we’re going to have to do is to count the lengths of the squares that go all the way around.
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We could call these squares units.
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Let’s start by measuring the perimeter of the kitchen.
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The longest side here is six units long, and this shorter side is two units long.
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Then we’ve got another long side of six and another shorter side of two.
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This is interesting, isn’t it?
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We’ve got two lots of six and two lots of two.
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This shows us what we know about rectangles, doesn’t it?
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They have two pairs of equal sides.
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We know that six plus two equals eight.
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And if we had another lot of six plus two or another lot of eight, we get a total of 16 units altogether.
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The distance all around the kitchen is 16 units.
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Now let’s measure the perimeter of Matthew’s bedroom.
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This side here is three squares long.
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Then this longer side is four squares long.
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Then just like before, we have another lot of three and another lot of four.
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We know that three plus four equals seven.
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And so if we had another lot of three plus four or another lot of seven, we get double seven, which is 14.
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The distance all around Matthew’s bedroom is 14 units.
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Now let’s measure the perimeter of David’s bedroom.
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This side here is four units long.
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This longest side along the top is six units long.
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We know that four and six make 10, don’t we?
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Can you guess what the whole perimeter is going to be?
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We have another side of four and another side of six.
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As we’ve said already, four plus six equals 10.
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And if we add another lot of four plus six or another lot of 10, we get double 10, which is 20.
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By counting the square lengths or the units all the way around these shaded rectangular rooms, we found which room has the largest perimeter.
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The perimeter of the kitchen is 16 units.
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The perimeter of Matthew’s bedroom is 14 units.
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But the perimeter of David’s bedroom is 20 units.
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Out of the three shaded rectangular rooms, the one that has the greatest perimeter is David’s bedroom.