Geometry box question

Question

An open-topped box is created out of a rectangular sheet of cardboard. The short side of the cardboard is 4/5 the length of the longer side. If a two-inch square is cut out of the corner and the volume of the box is 176in3, what are the dimensions of the original sheet of cardboard?

Answer 1

Let the length, breadth and height of the box be l,b and h respectively.

h = 2 inch

b = 4/5 * l

V = l*b*h

176 = l * (4/5)l * 2

l^2 = 110

l = sqrt(110)

and b = 4*sqrt(110)/5

So the length of the original sheet = sqrt(110) +4

and breatdh of the original sheet = 4*sqrt(110)/5 + 4