Q. A sq plate of some size is cut at 4 corners of same size and formed an open box. If dis box contains 128 ml of oil, what is d size of d size of d plate?

• Assume, side of original plate be = x
  and 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
  but height will not change,so, the height of the box = 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
• 11 years agoHelpfull: Yes(2) No(0)