 Welcome friends, so yet in yet another very interesting problem solving session we saw this question today and most of you have answered, tried to answer it and a few of you have taken a wrong approach altogether. Most of you have assumed wrong things and then you have tried to attempt this problem but now let us understand what this problem was and what should be the thinking process. So the question was that 1 inch squares are cut from the corners of this 5 inch square. So this was 5 inch square and 1 inch corner was cut out from the square and you have to find out the area in square inches of the largest square that can be fitted into the remaining space. Most of you have done this that you have considered EFGH as the largest square that could be fitted into this remaining space but you did not think of another square which could be of this type A, B, C, D. Most of you have also taken another assumption where you have joined these points, the midpoints and considered this to be the requisite square but it is not the case. So why because in that case if you join the midpoints there will still be some space left between the corners of the smaller square and I will show you what do I mean. Let us say if you are joining the midpoints and let us say this was all 1 inch square so if you join the midpoints like that, do not go by the accuracy of the diagram what I am trying to say is there will be some space left over here. So hence if you see this is the you are limiting the size of the square. Now if you could have brought this line which is highlighted here closer to this vertex, this this corner vertex so that they are in contact then you can actually maximize the square. So hence but if you increase the size then the square would just go out of the space isn't it? If you try to let us say this is the line and you try to move this in this direction then the square would be like that and then it would go out of the remaining space. So hence in that case what you need to do is you need to rotate this and hence once you rotate it this particular vertex these vertices will now come and fit it into the remaining space and if you see this is how the final figure would look like this correct. So this would be the largest area of the square. Now what are these smaller lengths we don't know but we actually don't require also to find it out to find this area. So what will be this area like? So very clearly you can see the area is nothing but area of square ABCD is nothing but area of square EFGH, EFGH plus the area of four triangles. What triangles? Area of triangle AEH plus area of triangle DHG and plus area of triangle CGF plus area of triangle BFE is it not? Now in all these if you notice due to symmetry all are equal in area and not only because of symmetry you can see that the base of all these triangles are same right. So for example in this case AEH, HE is the base so you can see HE is the base then in triangle DHG, HG is the base and CGF, GF is the base and your EBF or BFE, EF is the base and all these bases are equal right because all these are equal because all of them are nothing but five minus one minus one why this five and then you take this one off take this one off. All are three inches long and the height of all these triangles also if you see what is the height here if I have to mention the height this is the height is it in this case this is the height in this case this is the height in this case and this is the height in this case which is nothing but the distance between the two parallel lines right. So hence what is the height clearly the height of all these height is nothing but one inch one inch why because this line is equal to this side isn't it because if you can see notice this is a rectangle so hence this AE will be equal to sorry not AE this this height is equal to let us say let me highlight this so this height is equal to this side or this height is equal to this height like that right. So hence all the triangles will have the same base and same height now can we not find out the area then yes of course we can find out. So what is the area so area of square EFGH is nothing but three square three into three because EFGH EF this is three and this also is three so area of the square is three square plus what is the area of total sum of all the areas of the triangle will be nothing but four into why four into because all the areas have sorry all the triangles have same base and same height so half into base is three into height is one right. So hence it is six so nine plus six is equal to fifteen square inch so this is the solution so answer to this problem is that the area is fifteen square inch okay so in this case answer is C.