MNetters love a maths question

[noblegiraffe]

Here's a lovely maths question I saw on twitter the other day.

For a Y8 class.

Bear that in mind while you're thinking WTF?

It's not really about learning this as a fact ,though. And post GCSE maths isn't really much like this.

It's more of a puzzle that lets you apply what you know to a more complicated situation, and that's kind of fun when you see that a simple rule can actually let you do something quite hard like this, and kind of satisfying and fun when you work it out I didn't get it for a while, had to really think, but then I did see it. It wouldn't be something that we'd have ever been taught. The skills of problem solving, though, are generally useful in maths as well as other disciplines, so I can see why they include something like this as a puzzle for year 8

Just colour the small rectangle grey to match & then draw a line through the middle ☺️

You'd have to understand the properties of a line that bisects the middle of a rectangle will always split in two equal halves

Now that is thinking outside the box!

Best answer.

@Elephantstatue Are you an architect?

😂😂😂😂

Diagonal line (cuts in half without having to exactly measure).
White triangle irrelevant?

You need to have the same amount of grey on each side of your line so the white rectangle is relevant as it is not grey.

Have used my brains now (ie googled, found on Twitter). I shall not spoil it for others....though I liked someone'e rephrasing

I have a tray of brownies. Someone took a random piece out of the middle. How do I share the rest equally into 2 portions.

Aha! Thank you.

ah cool. I didn't get it. I love that it's such a generic solution - you could place the white rectangle anywhere, including along an edge, and it would still work. Thanks for this.

One of those ones that lets kids wow their parents!

A hint for anyone stuggling....(and it is in the question)...you can draw more than one line to help you get the answer.

My dh just instantly came up with what seems to be the sensible solution (hinted at by pp)

I assume that any line going through the centre point divides a rectangle in half, so the line that goes through the centre point of both rectangles divides both in half.

True for diagonals, verticals and horizontals, and looks right, but not going to try to prove it generally!

Not a formal proof, but draw a line through the middle parallel to one pair of sides.. Any other line through the middle will create symmetric shapes above and below that reference line!

I have a Cambridge maths degree. And I only got it after reading some of the hints!

Oh - the shame!

I'm confused!!!! Will the answer be shared?

What the jeff?! Just tell the rectangle thief to own up and put the stolen bit back.

Then divide in two.

Draw the diagonals on the white rectangle and again on the giant grey rectangle.
Now draw a line that does from one edge to another going through the two points where the diagonals cross.

Any line through the centrepoint of the rectangle splits it in half by area. So you have split both rectangles in half so the grey area is equal on both sides.
I expect someone will draw a picture and upload it in due course.

@TeenDivided I just did exactly what you said - is the blue line the divider???

Exactly.

Amazing. I would never have worked that out

Wow. I would have never got that.

Find the middle of each rectangle and then draw a line through both middles?

Well, I wouldn't have thought of that!