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The question is :-

A figure consist of five equal squares in the form of a cross .show how to divide it by two straight cuts into four equal figures which will fit together to form a square.

Please tell what would be our approach to solve the question ,I am confused what would be our steps to proceed,even i cant guess the first step (please clearly elaborate your steps) . It is a question under the chapter Triangle of an olympiad book so something must be related to triangles definitely.

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  • $\begingroup$ I saw the video its a nice video :) but can you tell that for a student like me how would i be able to think such a solution.. my exact question is that is there a method for these type of transformation problems? $\endgroup$ – Akshaj Bansal Jun 13 '19 at 15:34
  • $\begingroup$ @Ak19 In your solution figures are not congruent. $\endgroup$ – Michael Rozenberg Jun 13 '19 at 15:38
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You are hinted by the fact that if the pieces have equal area, they must have sides $\dfrac{\sqrt5}2$, which evokes the diagonal of $2\times1$ rectangles.

enter image description here

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    $\begingroup$ @AkshajBansal: do you mean that you don't see the cuts ? $\endgroup$ – Yves Daoust Jun 13 '19 at 16:49
  • $\begingroup$ @AkshajBansal: what is the diagonal of a $2\times1$ rectangle ? What is the area of the squares ? $\endgroup$ – Yves Daoust Jun 13 '19 at 18:04
  • $\begingroup$ Sorry for all that i got the question. Earlier i was thinking something else . Thanks :) $\endgroup$ – Akshaj Bansal Jun 13 '19 at 18:19
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This image illustrates how the requisite dissection arises naturally:

enter image description here

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