? 01-Secure Q A A rectangular piece of sheet metal is 8 inches longer than it is

Question

? 01-Secure Q A A rectangular piece of sheet metal is 8 inches longer than it is wide. From each cormer, a 1 x 1 inch square is cut out and the flaps are then folded up to form an open box. You are given that volume of the o Hint : Draw a diagram of the rectangular piece of sheet metal and list its dimensions. Then draw the 1 x 1 inch squares in each corner and the flaps, and list the di of the box. What is the length of the rectangular piece of sheet metal? ubmi Answer Tries 0/99 What is the width of the rectangular piece of sheet metal?

Explanation / Answer

Let the width and the length of the rectangular sheet be x inches and x+8 inches respectively. When , from eacch corner, a 1 inch x 1 inch square is cut and the flaps are made to make an open box, then the length, width and the height of the box are (x+8-2) = x+6 inches, x-2 inches and 1 inch respectively. Therefore, the volume of the box is V = (x+6)*(x-2)*1 = x2 +4x- 12 cubic inches. Hence, x2 +4x- 12 = 1833 or, x2 +4x -1845 = 0.On using the quadratic formula, we have x = [-4±?{(4)2-4*1*(-1845)}]/2*1 = [-4±?(16+7380)]/2 = (-4±?7396)/2 = (-4± 86)/2. Now, since x cannot be negative, we have x = (-4+86)/2 = 82/2 = 41.

Thus, the length of the rectangular piece of sheet metal is x+8 = 41+8 = 49 inches.

The width of the rectangular piece of sheet metal is x = 41 inches.

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