Video Transcript
Here is a rectangle. Select the rectangle that has the
same perimeter but a larger area than this one.
To begin with, in this question,
we’re given a picture of a rectangle. It’s labeled with a length of eight
centimeters and a width of four centimeters. And we know that the squares that
make up this rectangle must be one centimeter long because we can see that it’s
eight squares long and four squares wide. Now, underneath this we’re given
four more rectangles. And we’re told that we need to
select the rectangle that has the same perimeter but a larger area than our first
rectangle. Now we know that the perimeter of a
shape is the distance all around it.
So let’s find out what the
perimeter of our first rectangle is. As we’ve said already, its length
is eight centimeters, and its width is four centimeters. Eight and four is 12, so these two
sides together have a distance of 12 centimeters. But we need to double this amount
because we’ve got another side of eight centimeters and another side of four
centimeters. In other words, we can find the
perimeter by adding the length and the width together and then doubling it. Eight plus four is 12 and 12
doubled gives us a perimeter of 24 centimeters. So which of our possible answers
also has a perimeter of 24 centimeters?
The length of this first rectangle
is 11 centimeters, and its width is another one centimeter. So that’s 12 centimeters
altogether. But then, just like before, we’ve
got another length and another width, so we need to add together 11 and one and then
double it. And 12 doubled is 24. Although this rectangle looks a lot
different than our first one, it’s actually the same distance all the way
around. What about the second
rectangle? Its length is 10 centimeters; its
width is two centimeters. And 10 plus two is 12 again. And if we double 12, we get a
perimeter of 24. Do you notice that if we add
together the length and the width and they make 12, then we’re going to get a
perimeter of 24.
If we look at our next rectangle,
seven and five make 12. So this rectangle has the same
perimeter and so does the final rectangle. Nine plus three is 12. And if we had another nine and
another three, we get 24 centimeters. So in a way, this hasn’t really
helped us. We’ve still got four answers to
choose from. But at least it tells us something
about rectangles. They can have the same perimeter
but look very different. Now, we’re looking for a rectangle
that has the same perimeter but a larger area. And we know that the area of the
shape is the space inside it. And we can measure the space inside
these rectangles in square centimeters. We can do this just by counting the
squares inside them.
First of all, let’s find the area
of our first rectangle, the one we need to compare to. We can see that it’s made up of
four rows of squares and each row contains eight squares. And four times eight is a total of
32 square centimeters, so we’re looking for an area to beat this. The space inside our first
rectangle doesn’t look like it’s any bigger, does it? There are just 11 square
centimeters inside this shape. Our second rectangle is made up of
two rows, and each row contains 10 squares, so that’s 20 squares altogether. The area of this shape, 20 square
centimeters, is still less than 32.
Let’s keep looking. We can see inside our next
rectangle, there are five rows, and each row contains seven squares. And five times seven is a total of
35 square centimeters. This rectangle has more space
inside it than our first one. Looks like this might be the
correct answer. And if we look very quickly at our
final rectangle, we can see three rows of nine squares, which gives us an area of 27
square centimeters. This question shows us that even
though a rectangle may have the same perimeter as another one, they don’t always
have the same area. The rectangle that has the same
perimeter but a larger area than one with a length of eight centimeters and a width
of four centimeters is a rectangle that has a length of seven centimeters and a
width of five centimeters.
