Dividing a 5-Square Cross into 4 Equal Squares

[vaishakh]

A figure contains five equal squares in the form of a cross. Can you show how to divide this figure into four equal parts which will fit together to form a square

 

[AKG]

By "equal" do you mean "congruent" or "equal in area"?

 

[ceptimus]

Tricky. If the five original squares are unit squares, then the area of the square you have to form from them is 5. So the sides would have to be sqrt(5) long = 2.236 approximately. Here's a way you might do it - but the diagram isn't to scale.

 

[Joffe]

I posted the solution to this the other day but for some reason it has been removed, here it is again, not sure if it is the same as Ceptimus' as his attatchment is still pending.

 

[ceptimus]

The question said 'four equal parts'. Joffe's disection is ingenious, but the parts aren't equal.

As my attachment approval is still pending, here is a link to the same image hosted elsewhere.

http://www.mround.pwp.blueyonder.co.uk/physics/image/disection.gif

 

[Joffe]

Aha, I didn't read the question carefully enough, thanks for pointing that out Ceptimus. Whichever moderator deleted I think should have instead pointed out my error or at least PM'd me, rather rude I feel.