A square has a perimeter of 24
centimeters. Yvette cuts the square in half to
form two identical rectangles. Yvette says that the perimeter of
each of the rectangles is 12 centimeters because 24 divided by two equals 12. State whether Yvette is correct or
incorrect, giving reasons for your answer.
So first of all, what we know is
that we’ve got a square. And it has a perimeter of 24
centimeters. So then what we’re gonna do is
actually call the sides of the square 𝑥. We know that they’ll all be the
same because it’s a square. Well, to find 𝑥, what we’re gonna
do is we’re gonna take 24, which is our perimeter, and we divide it by four because
there are four sides. And this gives the value of six
centimeters. So we actually know that each of
the sides is going to be equal to six.
Well, in the question, what it also
says is that actually Yvette cuts the square into two identical rectangles. So what I’ve done is I’ve drawn a
dashed line to show where it’s gonna be cut. And then I’ve drawn our two
identical rectangles. Well, we can see that actually the
height of our rectangles is going to be the same as the length of the side of our
square. So that’s gonna be six.
However, the width of our
rectangles is going to be different. And that’s because actually the
width of our two rectangles, so we’ve actually got two widths, is made up of the one
side length from the square. So therefore, what we’ve had to do
is divide six by two because that’s the side length of the square, which gives us
three. So we can actually see that
actually the width of each of our rectangles is three, or three centimeters.
So now, what I can do is actually
work out what the perimeter of one of our rectangles is going to be. So it’s gonna be equal to three
plus six plus three plus six. And that will be the same for each
of our rectangles. Because obviously, they’re
identical. Which is gonna give us an answer of
18 centimeters. And that’s because three plus six
is nine. And nine plus three is 12. And 12 plus six is 18.
So now, if we actually look at what
Yvette said, Yvette said that the perimeter of each of the rectangles is 12
centimeters because 24 divided by two is 12. So the first thing we can do is
answer the first part of the question, which is state whether Yvette is correct or
incorrect. Well, Yvette is definitely
incorrect because we found the perimeter to be 18 centimeters not 12
And then, we have to look at the
second part of the question. The second part says: give reasons
for your answer. Well, the reason that Yvette is
incorrect, and we’ve already shown this, is that the process of dividing a square
into two identical rectangles halves the length of two of the sides but keeps the
two of them constant.