A square plot of some size , at four corners equal squares of some size are cut and is formed as open box. If this open box carries 128ml of oil. What is the size of the plate i.e. side

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A square plot of some size , at four corners equal squares of some size are cut and is formed as open box. If this open box carries 128ml of oil. What is the size of the plate i.e. side

all the answers are wrong it is 12
len * breadth * height must be 128
len = breadth since it is a square plot..
hence height = 2
len = 8 + 2 + 2 = 12 cm

let, side of original plate be =x
also, side of the square at the corners= a
so, when the square at the corner is cut off, the length of the box is=x-2a
similarly, the breadth of the box is=x-2a
the height of the box would be invariably=a
so, the dimension of the open box=(x-2a)*(x-2a)*a=a*(x-2a)^2
so, we need to factorize 128 so that we get a square term & an integer.
case 1. 128=2*2*2*2*2*2*2=(2*2*2*2*2)*2*2=32*2*2
so, a=32, x-2a=2, x=2*32+2=66
case 2. 128=2*2*2*2*2*2*2=(2*2*2)*(2*2)*(2*2)=8*4*4
so, a=8, x-2a=4, x=2*8+4=20
case 3. 128=2*2*2*2*2*2*2=2*(2*2*2)*(2*2*2)=2*8*8
so, a=2, x-2a=8, x=2*2+8=12
so, the possible values of the side of the original square plate are 66, 20 & 12
none of these match the answer options provided in a. , b. or c.
so, the correct choice is d. or none

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