Son (yr 4) has a homework ‘challenge’… I’m at a loss without going back to first principles i.e. cutting out the pieces, though some abstract thinking suggests there is no solution 😆 – otherwise the only thing I can think of is that the squares are used to form the perimeter of the rectangle, which will then be hollow..

I have 9 squares with sides of length 1cm, 4cm, 7cm, 8cm, 9cm, 10cm, 14cm, 15cm and 18cm. They can be fitted together to form a rectangle. What is the width and length of this rectangle? How do you know?

Is there something obvious I can’t think of?

Make the squares out of some pieces of paper and then fit them together

Work out the total area of the squares which will give you the area of the rectangle. Then work it out from that 😀

Year 4 sounds really tough, glad I got it out the way when I had a brain that worked properly

Work out the total area of the squares which will give you the area of the rectangle.

That’s what I thought but (unless I’ve been silly) the total area of the squares is 1056, which isn’t a multiple of 18. Gut feel is that the rectangle surely has a width of 18, but obviously not if 18 x something has to equal 1056?

Edit: of course I am assuming this rectangle has no “holes”, ie. all the rectangle is purely made of these squares. That isn’t specified is it?

Same as Munkster –

The total area doing that method would be 1056, and i can’t work out how to make that out of those shapes..
It’s annoying me now, i’m sat with cut out squares on my desk!

22 x 48

Daughter on the case

Well working out the total area (which you have done and is apparently 1056), then you can factorise it to find all the factors >= 18 (because as a minimum the 18 square needs to fit)…

Presumably only one of these has values that can be obtained from the sum of the values available.

That said, this seems rather sophisticated for what 9yr old maths…?

https://goo.gl/images/ZMIUK0

Sad when google replaces maths.

THat’s barely a rectangle TBH

THat’s barely a rectangle TBH

starting with the smallest square, I don’t see how the 1×1 square can ever be integrated, unless the rectangle is partially hollow, but can’t prove it. Which would mean that the rectangle must be partially hollow.

All instructions on the piece of paper have been given in the first post. It seems to be a ‘stretch’ task, but obviously no questions were asked in class when the work was handed out…

That said, this seems rather sophisticated for what 9yr old maths…?

That’s what I thought- originally I thought it was a piece of work given to his older sister.

Yay! but our 15×15 and 14×14 are labelled wrong. 22×23 rectangle.

Previous posters have pretty much nailed it. You need two factors that multiply to give the total area, and they both need to be at least 18. You should start by listing all the prime factors, e.g. 2x2x2x3x…whatever.

I was pretty good at maths as a child, don’t think I was doing this sort of stuff aged 9 though…if that’s what year 4 means (no kids myself no idea).

I think the idea is to get them to play with the physical squares. Or google “factor 1056 squares” and click images. Proving there are multiple solutions would be harder. Or no more solutions…

The link is actually very good. Might be where their teacher lifts the problems 😉 . I’ve been revising C1 with Teen2 this evening. Love a bit of sequences and series. Setting problems is surprisingly hard.

Where’s your 1×1?

Someone did their sums wrong that’s 506 not 1056 which makes it rather easier as 23 is a prime factor so there’s no choice, it’s just a matter of finding whether the shapes fit.

In the middle of the 7,8,9 & 10

What’s 506 and not 1056?

thecaptain – Member
Someone did their sums wrong that’s 506 not 1056 which makes it rather easier as 23 is a prime factor so there’s no choice, it’s just a matter of finding whether the shapes fit.

Its definitely 1056!

Also Wally, isn’t that a 32×33 rectangle? And 32 x 33 is 1056?

Oh yeah! It’s small. Being 1×1 I should have expected that..

It was the guy who said 22×23 who did his sums wrong 🙂

Yay! but our 15×15 and 14×14 are labelled wrong. 22×23 rectangle

Sure about that?

18+15 =
18+14 =

Whoops, I was rushing and had a clarinet one foot from my ear and continue to do so. I chose my forum name carefully..

That should be 33 x 32 surely?

Those cut outs don’t make a rectangle.
Top? edge is 18+14 = 32
Bottom edge is 15+10+9 = 34
Left edge is 18+15 = 33
Right edge is 14+8+9 = 31

That’s a… quadrilateral?

Those cut outs don’t make a rectangle.
Top? edge is 18+14 = 32
Bottom edge is 15+10+9 = 34
Left edge is 18+15 = 33
Right edge is 14+8+9 = 31

That’s a… quadrilateral?

POSTED 4 MINUTES AGO # EDIT DELETE UNDELETE LOOKUP WARN BAN MESSAGE REPORT-POST

Because

Yay! but our 15×15 and 14×14 are labelled wrong.

POSTED 4 MINUTES AGO # EDIT DELETE UNDELETE LOOKUP WARN BAN MESSAGE REPORT-POST

Bit harsh we’re all guilty of skim reading.

Ooooops! Copied too much. 😳