A box with no top is to be constructed from a piece of cardb

A box with no top is to be constructed from a piece of cardboard whose length measures 6 in more than its width. The box is to be formed by cutting squares that measure 2 on each side from the four corners and then folding the sides. If the volume of the box will be 100 in^3, what a the dimensions of the piece of cardboard?

Solution

length = 6 +width

So, let length l and width be w

So, l = (w+6)

Now square of 2 inch is cut from corners

So, length = (w+6)- 2 -2 = w +2

width = w -2 -2

height = 2 inch

So, volume = length*width*height = (w+2)(w-4)*2 = 110

(w+2)(w-4) = 55

w^2 -2w -8 =55

w^2 -2w - 63 =0

factorise : w^2 -9w +7w -63 =0

w(w -9) +7(w-9) =0

(w +7)(w-9) =0

w =-7 and w=9

Neglect -ve width

So, we have width w = 9 inch

length = w +6 = 15 inch