Problema Solution

a rectangular piece of sheet metal is 6 in. longer than than it's wide.A square piece that measures 3 in. on each side is cut out from each corner, then the sides are turned to make a box with volume 273 in^3. Find the length and width of the original piece of sheet metal.

Please draw with a diagram.

Answer provided by our tutors

let


l = the length of the original piece of sheet metal, l>0

w = the width of the original piece of sheet metal, w>0


a rectangular piece of sheet metal is 6 in. longer than than it's wide


l = w + 6


since 3 in. on each side is cut out from each corner the dimensions of the box will be:


l - 2*3, w - 2*3 and 3 thus the volume of the box is V = (l - 6)(w - 6)*3 that is


(l - 6)(w - 6)*3 = 273


by solving the system of equations


l = w + 6

(l - 6)(w - 6)*3 = 273


we find and consider only the positive solutions since l>0, w>0


l = 19 in


w = 13 in


the length and the width of the original piece of sheet metal are 19 in and 13 in respectfully.