A square plate of some size is cut at four corners. Equal squares of the same size are cut and is formed as open box. If this open box carries 128 ml of oil. What is the size of the side of the plate?

(a) 17
(b) 14
(c) 13
(d) None of these

• can u pls explain
• 13 years agoHelpfull: Yes(11) No(1)
• 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
• 11 years agoHelpfull: Yes(7) No(8)
• 10 ,12 or 34 units
  
  If side of square cut at corner= y & remaining length of a side of a plate=x
  Total length of a side of a square plate= x+y
  The dimensions of a box formed are length=x,breadth=x, height=y
  So volume of a box=x*x*y=x^2*y=128
  With three possible solutions,x=8,y=2 or x=4,y=8 or x=2,y=32
  So side of a square plate=x+y=10 or 12 or 34
• 10 years agoHelpfull: Yes(5) No(2)
• b
• 14 years agoHelpfull: Yes(1) No(10)