A rectangular piece of cardboard is 2 inches longer than it

A rectangular piece of cardboard is 2 inches longer than it is wide. From each corner, a 2×2 inch square is cut out and the flaps are then folded up to form an open box. You are given that volume of the open box is 96in^3.

What is the length of the rectangular piece of cardboard?

Solution

Let width be x

lenght = x+2

each corner, a 2×2 inch square is cut out and the flaps are then folded up to form an open box

height of box = 2

lenght = x +2-2-2 = x-2

width = x-2 -2 = x-4

Volume = l*b*h = (x-2)(x-4)*2

(x-2)(x-4)*2 = 96

(x-2)(x-4) =48

x^2 -6x - 40 =0

solve the quadratic: x = (6 +/-sqrt(36 +4*40)/2

we get x= 10, -4 Neglect -ve value of x

So, length = x+2 = 12 inches