Video: GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 5

GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 5

02:34

Video Transcript

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 centimeters.

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.

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