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.
