There is a door with length =8 and width =4. A wardrobe

Question

There is a door with length =8 and width =4. A wardrobe should be brought through this door. The dimensions of the wardrobe are the following: length=y, width =x and height=z, where z>y>x. Will this wardrobe pass through the door? 1) x+y+z<12 2) (x^2)+(y^2)+(z^2)<16

arjtryarjtry · Answer

can some one explain?

bhushangiri · Answer

For the thing to "not" go thru the door, length width and depth all need to be x,y,z --> 4+ i.e tending to 4 from positive side.. i.e slightly greater than 4. 
So if each is greater than 4 then x+y+z > 12. Has to be.
If x+y+z < 12 then atleast one side is less than 4, and so the wardrobe can go through door.

1) is sufficient.

Similar logic using square for 2)

hence D

arjtryarjtry · Answer

i think it has got something to do with the longest diagonal in a cuboid..
the longest lenght of the diagonal is given by[(a^2+b^2+c^2)]1/2, where a,b,c are length width and height respectively..
but it still does not help explain 1... :roll:

bhushangiri · Answer

No it has only to do with the length of sides. When the cupboard needs to be taken through the door, trying to get the diagonal through the door is the most cumbersome way to do it. Along the edges is the easiest. 
So go/no-go is decided by the l/w/d dimensions and not the diagonal dimension.

There is a door with length =8 and width =4. A wardrobe

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