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.