A maths reasoning question.

[WelshMoth]

I'm scratching my head as to how to tackle this:

See pic.

Consider the black and white shape in the pic. Which statement is correct?

A) the perimeter of the black shape is the largest

B) the perimeter of the white shape is the largest

C) the perimeter of both is equal.

Help!

No idea where the 'will' came from....

The area looks like it should be equal, but the actual perimeter looks like the black should be bigger.

I think you might have the meaning of perimeter and area mixed up. The perimeter is the same as each colour shape has 16 equal sides but the areas are different.

The perimeters are equal because they're the same line!

Yes each section of line has white on one side and black on the other, so they have to have an equal perimeter.

Perimeter = distance around the edge.

Place a length of string all along the edge of the shape (in your mind). Measure it. That's the perimeter.

You'll find that the string is the same length for the white and black shapes.....because they're exactly the same lengths....because they're exactly the same lines.

Tbh I'm gobsmacked this question is being asked of a 13yo.

Sorry. I don't mean to be a dick. Maybe the question isn't actually about maths reasoning. It's probably just a test of whether you know what "perimeter" means. That makes more sense.

I can see the logic behind saying there are 18 of each shape, and therefore the perimeters where the items touch us identical. But, and I'm asking not from a point of knowledge, there is more black around the perimeter of the picture square than white. Does this mean the black has a greater perimeter due to the amount of black perimeter on none touching lines?

7Salmon don't worry - I see what you mean - DH and I are having difficulty explaining this one.

I know that I should apply logic, but the black area perimeter appears bigger?! Still can't grasp this

surely 'largest' should be 'longest'? And ' the perimeterS of both ARE equal'?

winterheatwave I'm taking the question to mean take one of the black tiles and one of the white tiles in isolation. Which one has the greater perimeter? But I agree it's open to another interpretation. I think they've put the bigger picture to show the tesselation.

OP imagine if you started with square tiles in a black and white chequerboard. Happy that the perimeter of the black and white squares would be identical?

Now imagine the sides are made of elastic. Mentally kink one of the sides to make the boundary line between the black and white. It's not much off straight, it's going from to /\_ . Can you see that by doing that, you are adding equally to the perimeter of the black shape and the white shape? Your elastic has got a bit longer but it still has white on one side and black on the other. There can't be a longer measurement of black on one side than there is white on the other. It would be like reading 2 different measurements off different sides of a tape measure.

(The areas are affected differently. The new triangle created flips from white to black so the area of white decreases and the area of black increases, but you need to look with different eyes if you are thinking about perimeter only,)

Ugh, editor has been too clever with my lines. I'll try again. Making the link would take it from

to
/ \

I am way too invested in this thread

Cwg fair cop guv.
I was translating from a different language. Lost in translation somewhat. 'Longest' indeed.

I blame the other error on my phone.

C

They share the little side which means they are the same length. Because they have the same number of sides,16 that would make the perimeter of each shape the same.

Draw a little x on a shared side.

Perimeter of black= x+x+x.... 16 tmes. Or 16 * x

Perimeter of white = x++x+.... 16 times or 16 * x

The reasoning involved is this: you have black squares and white squares of equal area and perimeter. You then draw a little notch into each white square- the area of the white squares is now less, but each length of the square’s side has been increased by the same amount, so the perimeter remains equal.

Perimeter - equal.

(Area - black shape is bigger than white)

Maybe it helps to understand if you think about what it means if the perimeters are not the same?

Imagine the white shape and the black shape both as squares with wiggly edges. If the lengths of the white and black edges, including wiggles, were not equal, then it would not be possible to join them up to form the pattern without having a bit of one of the edges left over. So all the edges must be the same length.

This means the perimeters are the same too.